Czech Science Foundation – Part C: Project Description
Applicant: Pavel Cejnar
Name of the project: STATISTICAL APPROACHES TO QUANTUM MANY-BODY SYSTEMS
1. INTRODUCTION
This project is focused on the theoretical and experimental investigation of diverse statistical
properties of complex quantum systems that consist of a large number of strongly interacting
particles. Although exact theoretical predictions for such systems are hindered by the well-known
problem of computational complexity, various approaches based on general assumptions of
statistical physics are very powerful. These approaches are of our main interest here.
The researchers involved in the project share a common background of nuclear physics. This
is convenient since the nucleus represents an essential example of a complex many-body system.
Nevertheless, one of the intentions of this project is to apply the statistical many-body methods in a
broader field – besides nuclei also in quantum optical systems, atomic and molecular systems,
mesoscopic structures etc.
The present proposal consists of three separate but interrelated topics. Below we present a
short description of each part and give basic information on the research team and its recent
achievements. (References to publications of our team are printed in bold.)
2. TOPICS, AIMS, METHODS
Topic A: DYNAMICAL SYMMETRIES AND QUANTUM PHASE TRANSITIONS
This part of our project is focused on the theoretical study of quantum critical effects in
transitions between dynamical symmetries of various models describing collective dynamics of
many-body systems. Quantum phase transitions (QPTs) [Ca10] bear close similarities to thermal
phase transitions but they are driven by non-thermal interaction parameters of the Hamiltonian.
QPTs in the collective models have some specific features. One of them is an extensive application of
group-theoretical methods and the derived concepts of quasi, partial or critical dynamical
symmetries [Ro10]. For a systematic description of recent progress in this field see our reviews
[Ce09, Ce10]. Our analyses will be focused on the QPTs in various collective models whose domain of
applicability ranges from nuclear and molecular physics [Ia87,Ro10,Fr05] to quantum optics [Or08].
Subtopic A1: Signatures of excited-state quantum phase transitions
(P. Cejnar and M. Macek in collaboration with P. Stránský from UNAM, P. Pérez-Fernández
and A. Relaño from CSIC/UAM Madrid and A. Leviatan from Hebrew Univ. Jerusalem)
Algebraic models describing collective dynamics differ from the microscopic models by
selecting only a small number of relevant degrees of freedom which are independent of the system’s
size. This implies that the thermodynamic limit of the system coincides with the classical limit, the
related phase transitions being rooted entirely in the classical Hamiltonian, implying certain universal
features. In particular, the ground-state QPTs follow from non-analytic evolutions of the classical
equilibrium point with the control parameter and can be alternatively described within the classical
Landau theory of phase transitions [Jo02,Ce03a,b] and the catastrophe theory [Lo96,Ce07b].
The excited-state QPTs, which is a novel concept introduced in [Ce06,Ca08,Ce08], are caused
by non-analyticities of classical dynamics connected with anomalous changes of the energy manifold
in the phase space. Such transitions are close analogues of thermodynamic phase transitions [Ka08]
but low dimensions of the phase space lead to rather non-standard transition types and surprising
thermalization properties. We want to continue in our ongoing investigation of excited-state QPTs in
the framework of generalized interacting boson models [Ia87,Fr05], especially with the aid of socalled intrinsic Hamiltonian [Le07]. Our preliminary analyses show that the spectrum of this model
exhibits some new types of critical features, which we intend to explore.
However, even more important focus of this part of the project is to classify the excited-state
QPTs in a larger set of low-dimensional (collective) systems and to establish their key signatures. Our
recent work [Pe11a,b] devoted to the models known in quantum optics (the Dicke model and its
integrable relatives) disclosed that excited-state QPTs have (besides their known impact on the level
density and level dynamics) also strong dynamical consequences. In particular, we observed an
exceptionally fast decay of correlations with the initial state after a quantum quench to the critical
excited region. This represents a viable path for an experimental identification of these effects in
fine-tuned artificial quantum systems (see cf. [Ba10]).
One of the aims is to extend these studies to other model systems (like the two-photon Dicke
model [Em02] and a generalized Jahn-Teller model of molecular physics [Bi00]). In addition, we plan
to analyze a wider variety of signatures of excited-state QPTs, particularly those related to quantum
entanglement and decoherence [Ca10,Pe09]. Our preliminary analytical and numerical calculations
indicate that the entanglement shows rather singular properties in the critical excitation energy
region. This effect, which concerns “static” entanglement (in the energy eigenstates) as well as the
“dynamic” one (in the evolution of the initially separable states), is in contrast to the semiclassical
expectation that genuine quantum features of the system become irrelevant as the excitation energy
grows. The importance of these studies is underlined by their possible application in quantum
information technologies, which are all based on the quantum entanglement [Ni00].
Subtopic A2: Mechanism of QPTs and complex extensions
[P. Cejnar in collaboration with P. Stránský (UNAM Mexico) and J. Dukelsky (CSIC Madrid)]
The mechanism underlying thermal phase transitions is connected with an accumulation of
zeros of the canonical or grandcanonical partition function in the plane of complex-extended
temperature or fugacity near the critical point on the real axis [Ya52,Bo00]. As shown in our works
[Ce05,Ce07a], a similar concept applies also in QPTs, where instead of complex zeros we consider
non-hermitian degeneracies of the quantum Hamiltonian (so called exceptional or branch points) in a
complex-exteded plane of the control parameter. An important role in the description of these
degeneracies is played by an analogy with two-dimensional electrostatic problems.
We intend to study the accumulation of branch points near the real control-parameter axis in
various integrable and nonintegrable models (see Subtopic A1). We will focus on the differences
between the accumulation rates for transitions of different types (orders). An important open
problem remains to be the connection between branch points located on higher Riemann sheets
(those corresponding to excited states) and complex zeros of partition function for the corresponding
temperature (the link between thermal and quantum phase transitions for excited states). We also
want to explore the connection between the electrostatic analogy for the branch points and a similar
method developed within the Richardson-Gaudin models for many-body systems with pairing
interactions [Du04].
Topic B: COLLECTIVE MODES AND STRENGTH FUNCTIONS
This part of the project is aimed at the theoretical and experimental investigation of nuclear
collective motions at high energies where the collective modes are fragmented into a large number
of excited states and only the statistical type of description is achievable. In particular, we want to
study giant resonances corresponding to specific collective motions of nucleons inside the nucleus
[Ha01]. Information on these modes, averaged over a number of individual excited states, is
contained in so-called strength functions of the gamma and beta types, which describe averaged
decay widths (electromagnetic and weak, respectively) of excited nuclear states. It should be
stressed that a detailed knowledge of the strength functions is rather important for nuclear
astrophysics as well as for the future development of nuclear technologies [Ba05].
Subtopic B1: Theoretical description of collective modes
(J. Kvasil,F. Knapp and P. Veselý in collaboration with V. Nesterenko from the JINR Dubna,
P.-G. Reinhard from the Erlangen University and N.Lo Iudice from the Naples University)
The collective nuclear motion in medium-mass and heavy nuclei cannot be analyzed using
the ab-initio approaches (like the no-core-large scale shell-model calculations [Na09,Ca05]) because
of enormous increase of the configuration space. Instead, the Random Phase Approximation (RPA)
[Ri80] built on the Hartree-Fock-Bogolyubov (HFB) approach is applied, starting with some effective
nucleon-nucleon interaction, or the corresponding density functional (see, e.g., [Be03,St07,Li08]).
However, fully self-consistent RPA calculations with a realistic effective interaction are feasible only
up to medium-mass nuclei. Heavy (especially deformed) nuclei yield too large matrices of selfconsistent two-body residual interaction. One of the methods to effectively bypass this problem is
the separable RPA (SRPA), suggested in our paper [Ne02] and subsequently used in [Ne06,Kl08,
Ve09,Ne10,Kv11a] for the description of electric and magnetic giant resonances (E1, E2 and M1) in
heavy nuclei.
In the present project, we plan to continue in the application of the SRPA method to the
evaluation of radiative (gamma-ray) strength functions (RSFs). We want to apply the method in
specific heavy nuclei where a comparison with experiment is possible, and also to extend the
calculations to the gradually opening domain of superheavy nuclei. Special attention will be paid to
the so called E1 pygmy resonance (E1PR), which has been recently a subject of intense research
[Li08,Is11]. We intend to focus mainly on the vortex character of nuclear motion in the Pygmy region
of excitation energy, using the approach developed in our recent paper [Kv11b] based on the
concept proposed in [Ra87]. The method allows us to treat the vortex, toroidal and compression
modes of nuclear motion on the same theoretical footing.
We plan to extend the SRPA method to the description of beta decay processes [Ha01], in
particular, to include the Gamow-Teller (GT) transitions and to investigate the influence of time-odd
densities, tensor and other terms in the Skyrme functional on time-odd GT excitations. Moreover, we
intend to use the method to calculate probabilities of double-beta decays of heavy nuclei.
The RPA, which is based on the harmonic approximation, captures basic features of low- and
high-energy vibrational collective modes. However, numerous anharmonic effects require
approaches beyond the RPA [Pa10]. One of such approaches, the multiphonon method, was
suggested in our papers [An07,An08] and recently further elaborated in [Bi12a]. We plan to apply
this method in the connection with modern nucleon-nucleon potentials (Argonne, CDBonn, N3LO)
and different renormalization schemes of bare nucleon-nucleon interaction (V low-k, G-matrix etc.)
and to study whether these potentials can be used for the description of giant resonances.
In parallel to the above-described research we intend to continue in the recently initiated
program of extended shell model calculations in medium-mass nuclei. Our approach, based on an
improved “importance truncation” diagonalization technique, was tested in Xe nuclei [Bi11] and its
potential was further demonstrated in N=80 isotones [Bi12b]. Application in other isotopic and
isotonic chains is planned. Moreover, we intend to progress in the development of our own version
of a computer code for no-core shell-model calculations, which would further enlarge the
applicability of the “importance truncation“ scheme.
Subtopic B2: Experimental radiative strength functions
(F. Bečvář, M. Krtička, J. Kroll, S. Valenta in collaboration with G. Mitchell from North
Carolina State Univ., J. Ullmann from the Los Alamos National Lab., I. Tomandl from NPI Řež, R.
Schwengner from the HZDR Dresden-Rossendorf, M. Guttormsen from the Oslo Univ., and L.
Bernstein from Lawrence Berkeley National Lab.)
Experimental information on the radiative decay of highly excited states in medium-mass and
heavy nuclei (in the region around the threshold for particle emission and below) is rather restricted.
These decays are subject to intense experimental study with the aid of various nuclear reactions, like
the inelastic photon scattering [Ru08], charged particle induced reactions [Gu05] or the capture of
thermal [Kr04,Kr09] and resonance [Sh09] neutrons. For the description of gamma-decay
probabilities at these energies, the RSF concept is applied. Apart from microscopic calculations, a
large number of phenomenological models is available. The aim of present experimental effort is to
put some constraints on these models. Moreover, as the data on RSFs obtained from different
reactions are not fully consistent [Kr10], it is necessary to perform more detailed and sophisticated
data processing and to realize new experiments in a broader region of nuclei. Theoretical approaches
outlined under Subtopic B1 will help to select the relevant models in various nuclei.
Our interest is mainly (but not exclusively) focused on the data coming from the radiative
neutron capture. The importance of this reaction (besides its relevance in the astrophysical and
technological applications) follows from the precise knowledge of the initial state and the possibility
to study its decays to a large number of final states. We plan to use primarily the following two
experimental setups: (1) The first is designed to measure two-step gamma cascades following the
thermal neutron capture. The device, using a two-photon coincidence technique with a pair of HPGe
detectors, is built on the research reactor in the NPI at Řež near Prague [Ho96]. Data from this
experiment proved that the scissors mode (a magnetic dipole excitation in deformed nuclei) is build
also on excited states [Kr04]. We intend to continue in this type of experiments to obtain new data
on the M1 as well as E1 strengths in a broader region of rare earth isotopes nuclei. (2) The second
setup is built on the pulse neutron source LANSCE in Los Alamos where photons are measured with
the DANCE detector. The DANCE detector is a highly segmented calorimeter which consists of 160
BaF2 crystals. It is used mainly for the detection of gamma rays produced in the capture of resonance
neutrons [Sh09,Ch11]. The spectra measured in these experiments allow one to get information on
the decays of neutron resonances with various spins and parities.
It is assumed that within this project data from both these experimental setups will be
processed. Special attention will be paid to three different regions of the periodic table: (a) Nuclei
with A<100. Recent results from charged-particle induced reactions indicated that RSFs in these
nuclei are strongly enhanced at low photon energies (below about 3 MeV) [Gu05,Wi12]. Contrary to
this, data from radiative neutron capture indicate that a possible enhancement at these energies can
only be very weak [Kr08a,Sh09]. In addition, these nuclei can serve as a test of applicability of the
statistical approach to nuclear decays. (b) Deformed, particularly rare-earth nuclei. The study of the
M1 scissors mode is planned here. In particular, information on the behavior of this mode in odd and
odd-odd nuclei is needed. In addition to experimental data from the two above described setups, a
proposal for measurement of three-step gamma cascades following thermal neutron capture in 161Dy
using the EXOGAM detector array has been submitted. (c) Nuclei with A=190-200. An indication
exists that the RSF shape in this mass region significantly differs from the other mass regions [Kr06].
Members of the research team will also continue in their collaboration with institutions
which study the RSFs using different types of reactions, specifically the photon scattering reactions
[Ru08] and charged-particle induced reactions [Gu11,La11a,Wi12]. Data from these resources
provide important complementary information on radiative decays of highly excited nuclei and will
be considered in the interpretation of the results from neutron capture.
Topic C: QUANTUM CHAOS AND ITS SPECTRAL SIGNATURES
In this part of our project we plan to study – from the theoretical and partly also
experimental sides – various quantum manifestations of chaos in many-body systems. Traditional
definition of chaos in quantum systems is related to correlations in energy spectra [St99], but
alternative dynamical approaches were formulated in terms of fidelity [Pe84a], decoherence [Zu94]
and other concepts. Nuclei, as highly complex quantum objects, as well as the models describing
them are almost ideally suited for the investigation of quantum chaos.
Subtopic C1: Random matrix theory
(Z. Pluhař in collaboration with H.A.. Weidenmüller et al. from MPI Heidelberg)
Gaussian ensembles of real symmetric (or Hermitian) random matrices [Me04], introduced
originally in connection with the statistical description of neutron resonances in nuclei, became a
basis for the definition of quantum chaos [St99]. Although the original types of ensembles, named
GOE (or GUE), reproduce well spectral correlations in quantum chaotic systems, they do not capture
realistic forms of many-body Hamiltonians, which are usually much sparser due to a specific
character of interactions. This problem is addressed by the introduction of so-called embedded
ensembles of random matrices with two-body (or k-body) interactions [Pl02,Pa07] and by various
types of constrained ensembles [Pa06]. An important task is to determine the conditions for the
validity of the Wigner-Dyson statistics in the spectra generated by these ensembles and to prove
their ergodicity [Pl00a,b].
We plan to continue in the theoretical research of nonstandard types of random-matrix
ensembles, namely the embedded, constrained and so-called deformed ones. The work was initiated
in [Pl02,Pa06,Pl09,Pa11]. We also intend to analyze properties of special ensembles with dominant
diagonal matrix elements. These are suitable for the description of nearly integrable systems and
may help to better understand the transition between order and chaos.
Subtopic C2: Experimental tests with neutron resonances
(F. Bečvář, M. Krtička, J. Kroll and S. Valenta in collaboration with P. Koehler from ORNL)
For decades, it was believed that fluctuation properties of transition amplitudes from nuclear
states near neutron separation energy in medium-mass and heavy nuclei were consistent with the
GOE predictions. However, recent evidence [Ko10] of non-statistical effects in the behavior of
neutron resonances (neutron decay widths violating the Porter-Thomas distribution), in which
members of our group participated, seems to change this paradigm. In the present project we plan to
extend the investigation of these effects.
First, we intend to theoretically analyze various consequences of the modified distribution of
neutron-resonance decay widths (such as changes in the percentage of resonance states which are
under the detection limits of various types of experiments) as well as possible origins of the non-GOE
behavior (based, e.g., on an interaction with the continuum [Ce11]).
Second, we plan to experimentally test a possible violation of the Porter-Thomas distribution
in different decay channels. Specifically, experiments related to study of distributions of intensities of
primary gamma-ray transitions from resonance neutron capture are presently under consideration at
the Geel linear accelerator GELINA.
Finally, secondary gamma transitions in the cascade decay of the compound nucleus
produced by neutron capture or other types of reactions can also be used for testing the validity of
the GOE assumptions at lower energies. Different types of fluctuation properties of the radiative
transition amplitudes can be built into the Monte Carlo code DICEBOX [Be98]. Results of simulations
can be compared with the actual spectra of gamma-rays measured in various nuclear reactions.
Subtopic C3: Chaos in collective degrees of freedom
(P. Cejnar, M. Macek and J. Dobeš in collaboration with P. Stránský and A. Frank from UNAM
Mexico, A. Relaño, R. Molina from CSIC/UAM Madrid, A. Leviatan from Hebrew Univ.
Jerusalem)
In our previous work it has been shown that collective models of nuclear dynamics, namely
the geometric model [Ro10] and the interacting boson model [Ia87], exhibit surprisingly complex
structures of competing regular and chaotic dynamics [Ce98a,b,Jo04,Ce04a,St06,Ma07,
St09a,b,Ma09,Ce11]. The classical and quantum measures of chaos in these models depend
sensitively on control parameters and energy, which constitutes an ideal environment to probe
various new theoretical descriptions, which are complementary to the traditional approach based on
random matrices. We have already applied some of such new descriptions, namely the long-range
spectral correlations measured by the power distribution of the Fourier transformed energy
spectrum [Re02,St10,La11b], and the method of spectral lattices disclosing correlations between the
energy spectrum and some features of wave functions [Pe84b,St09b,Ma07,Ma10b]. We plan to
employ both these concepts in a wider context.
The method of spectral lattices will be applied particularly in connection with the notion of
the quasi dynamical symmetry [Ro04]. Our analyses [Ma10a,b] within the interacting boson model
with the simple form of Hamiltonian showed that regular domains of intrinsic excitations – even
those at very high excitation energies – support the formation of rotational bands, which suggests
the existence of a peculiar form of a quasi dynamical symmetry in the high-energy region. We would
like to explore this phenomenon on a more general ground, using different Hamiltonians and other
types of quasi dynamical symmetries. In particular, we have already initiated the analysis of the
interacting-boson model Hamiltonian based on the intrinsic formalism [Le07]. The method of spectral
lattices is very helpful in these studies since it allows one to quickly distinguish classes of eigenstates
subject to different types of approximate symmetry.
The Fourier analyses of unfolded energy spectra [Mo11] will be applied in other model
systems, e.g., in the quantized coupled-pendulum and related models. An interpretation of results in
terms of spectral autocorrelation functions will be considered [La11b]. We will also focus on the
competition of regular and chaotic modes of motions in first-order quantum phase transitions within
the region of coexisting quantum phases. This is important for the classification of low-energy
collective modes in nuclei [Ma11]. Following our preliminary analysis of some quantum-optical
models [Pe11b], we also want to clarify the role of chaos in excited-state QPTs (see Topic A).
3. MEMBERS OF THE RESEARCH TEAM:
Our team consists of 10 regular employees (including 3 former PhD students, who are now on
postdoctoral positions abroad but keep partial contracts and collaboration in our institution) and 4
PhD students –see the list below. In the course of the project we plan to involve about 3-4 new PhD
students (at present, there are several Bc and MSc students involved in the work of our group). We
also intend to take advantage of the existing collaborations with foreign experts listed under each
partial topic in Sec.2. The present team members are as follows:
Pavel Cejnar (*1964) the main applicant
PhD. in nuclear physics in 1995 at the Charles Univ. in Prague. Habilitation in 2004. Doctor of Science
(DSc.) in 2010. Employed at the Faculty of Math. and Phys. as a docent (associate prof.).
Long-term stays abroad: Univ. Fribourg (Switzerland) 1991-2, 1994-5, Univ. Stellenbosch (South
Africa) 2000-1, ECT* Trento (Italy) 2006,7. Publications: 54 papers in journals with IF and 22
contributions in conference proceedings. 888 citations. H-index=20. Coauthor of review articles in
Rev. Mod. Phys. [Ce10] and Prog. Nucl. Part. Phys. [Ce09]. Most important papers: [Ce98a,Ce01,Jo02,
Ce03a,Ce04a,Ce06,Ce07a,Ca08,Pe11a]
Jan Dobeš (*1944) a joint applicant (for the NPI Řež)
Ph.D. in nuclear physics in 1973 at the Czech Technical Univ. in Prague. Director of the Nuclear
Physics Institute of the Czech Academy of Sciences since 1998. Long-term stays abroad: JINR Dubna
(USSR) 1976, Univ. Stellenbosch (South Africa) 1993. Publications: 54 papers in journals with IF and 7
contributions in conference proceedings. 598 citations. H-index=14. Most important relevant papers:
[Do98,Ce06,Ma07,Ma09,Ma10a,b,Ma11]
Jan Kvasil (*1950)
PhD. in nuclear physics in 1978 at the Charles Univ. in Prague. Doctor of Science (DrSc.) in 1988.
Full professor at the Faculty of Math. and Phys. since 1993. Long-term stays abroad: JINR Dubna
(USSR) 1980-5, Florida State Univ. (USA) 1987,91, Ludwig-Maxmill. Univ. Munchen (Germany) 1992-3,
Univ. of Naples (Italy) 1996,8,2000. Publications: 114 papers in journals with IF and 27 contributions
in conference proceedings. 813 citations. H-index=14. Coauthor of review article in Rev. Mod. Phys.
[Ja98]. Most important papers: [Kv98,Ne02,Kv07a,An08,Ve09,Ne10,Kv11b]
Milan Krtička (*1974)
PhD. in nuclear physics in 2002 at the Charles Univ. in Prague. Habilitation in 2011. Employed
at the Faculty of Math. and Phys. as a docent (assistant prof.). Long-term stays abroad: Oak Ridge
National Lab. (USA) 2003, Lawrence Livermore National Lab. (USA) 2005,6,7, Los Alamos National
Lab. (USA) 2008,10. Publications: 79 papers in journals with IF and 49 contributions in conference
proceedings. 507 citations. H-index=13. Most important papers:
[Bo99,Wi01,Za02,Kr04,Wi06a,b,Ko10,Wi12]
František Bečvář (*1937)
PhD. in nuclear physics in 1975 at the Czech Technical Univ. in Prague. Doctor of Science (DrSc.) in
1992. Habilitation in 1999 at the Charles Univ. in Prague. Employed at the Faculty of Math. and Phys.
as a research scientist. Long-term stays abroad: Dubna (USSR) 1966-74, 79-83, Brookhaven National
Lab. (USA) 1970,1980. Publications: 122 papers in journals with IF and 60 contributions in conference
proceedings. 1130 citations. H-index=18. Most important papers: [An98,Be98,Wi01,Kr04,Be08,Ko10]
František Knapp (*1979)
PhD. in nuclear physics in 2008 at the Charles Univ. in Prague (with J. Kvasil). Employed at the Faculty
of Math. and Phys. as an assistant prof. Long-term stays abroad: University of Naples (Italy) 20092010. Publications: 14 papers in journals with IF and 11 contributions in conference proceedings. 34
citations. H-index=4. Most important papers: [Kv07a, Kv07c,An07,An08,Bi11,Bi12a]
Michal Macek (*1981)
PhD. in nuclear physics in 2010 at the Charles Univ. in Prague (with P.Cejnar). Presently a
postdoctoral fellow at Hebrew Univ. in Jerusalem (Israel). During the stay abroad the collaboration
with our group is maintained (a partial contract, common publications) and after the return we count
on his full integration back into the group. Publications: 14 papers in journals with IF and 3
contributions in conference proceedings. 135 citations. H-index=6. Most important papers: [Ma06a,
Ma07,Ma09,Ma10a,b]
Petr Veselý (*1982)
PhD. in nuclear physics in 2008 at the Charles Univ. in Prague (with J. Kvasil). 2008-11 postdoctoral
fellow in Jyvaskyla University (Finland), presently postdoc in Univ. Naples (Italy). During the stay
abroad the collaboration with our group is maintained (a partial contract, common publications) and
after the return we count on his full integration back into the group. Publications: 12 papers in
journal with IF and 2 contributions in conference proceedings. 87 citations. H-index=6. Most
important papers: [Ne06,Ne10,Ve09]
Zdeněk Pluhař (*1937)
PhD. in nuclear physics in 1967 at the Czech Technical University in Prague. Habilitation in 1976.
Partial contract at the Faculty of Math. and Phys. of the Charles Univ. in Prague. Long-term stays
abroad: JINR Dubna (USSR) 1963-5, Technical Univ. Braunschweig (Germany) 1975,79, MPI
Heidelberg (Germany) 1985,2000-1. Publications: 26 papers in journals with IF. 194 citations.
H-index=6. Most important relevant papers: [Pl94,95,Pl00a,b,Pl02,Pa06,Pl09,Pa11]
Jiří Kroll (*1985)
PhD.student (3rdyear) at the Faculty of Math. and Phys. of the Charles Univ. (with M.Krtička).
Publications: 2 papers in journals with IF.
Daniel Božík (*1986)
PhD.student (3rdyear) at the Faculty of Math.and Phys. of the Charles Univ. (with J.Kvasil).
Publication: 1 paper in journal with IF
Stanislav Valenta (*1986)
PhD.student (2nd year) at the Faculty of Math. and Phys. of the Charles Univ. (with M. Krtička)
Anton Repko (*1987)
PhD.student (2nd year) at the Faculty of Math.and Phys. of the Charles Univ. (with J.Kvasil).
4. RELEVANT PUBLICATIONS OF THE RESEARCH TEAM:
[An98] W. Andrejtscheff,… F. Bečvář et al., Physics Letters B 437 (1998) 249
[An07] F. Andreozzi, F. Knapp, N.Lo Iudice, A. Porrino, J. Kvasil, Physical Review C 75 (2007) 044312
[An08] F. Andreozzi, F. Knapp, N.Lo Iudice, A. Porrino, J. Kvasil, Physical Review C 78 (2008) 054308
[Bi11] D. Bianco, F. Andreozzi, N.Lo Iudice, A.Porrino, F. Knapp, Journal of Physics G 38 (2011) 025103
[Bi12a] D. Bianco, F. Knapp, N. Lo Iudice, F. Andreozzi, A. Porrino, Physical Review C 85 (2012) 014313
[Bi12b] D. Bianco, F. Andreozzi, N.Lo Iudice, A. Porrino, F. Knapp, Physical Review C 85 (2012) 034332
[Bo99] H.G. Börner, … M.Krtička et al., Physical Review C 59 (1999) 2432
[Be98] F. Bečvář, Nuclear Instruments & Methods in Phys.Res. A 417 (1998) 434
[Be07] F. Bečvář, … M. Krtička et al., Nuclear Instruments & Methods in Phys.Res. B 261 (2007) 930
[Be08] F. Bečvář, J. Čížek, I. Procházka, Applied Surface Science 255 (2008) 111
[Ca08] M.A. Caprio, P. Cejnar, F. Iachello, Annals of Physics (N.Y.) 323 (2008) 1106
[Ce98a,b] P. Cejnar, J. Jolie, Physics Letters B 420 (1998) 241; Physical Review E 58 (1998) 387
[Ce00] P. Cejnar, J. Jolie, Physical Review E 61 (2000) 6237
[Ce01] P. Cejnar, V. Zelevinsky, V.V. Sokolov, Physical Review E 63 (2001) 036127
[Ce03a] P. Cejnar, Physical Review Letters 90 (2003) 112501
[Ce03b] P. Cejnar, S. Heinze, J. Jolie, Physical Review C 68 (2003) 034326
[Ce04a] P. Cejnar, P. Stránský, Physical Review Letters 93 (2004) 102502
[Ce04b] P. Cejnar, J. Jolie, Physical Review C 69 (2004) 011301(R)
[Ce05] P. Cejnar, S. Heinze, J. Dobeš, Physical Review C 71 (2005) 011304(R)
[Ce06] P. Cejnar, M. Macek, S. Heinze, J. Jolie, J. Dobeš, Journal of Physics A 39 (2006) L515
[Ce07a] P. Cejnar, S. Heinze, M. Macek, Physical Review Letters 99 (2007) 100601
[Ce07b] P. Cejnar, F. Iachello, Journal of Physics A 40 (2007) 581
[Ce08] P. Cejnar, P. Stránský, Physical Review E 78 (2008) 031130
[Ce09] P. Cejnar, J. Jolie, Progress in Particle and Nuclear Physics 62 (2009) 210
[Ce10] P. Cejnar, J. Jolie, R.F. Casten, Reviews of Modern Physics 82 (2010) 2155
[Ce11] P. Cejnar, P. Stránský, M. Macek, Nuclear Physics News 21 (2011) 22
[Ch11] A. Chyzh,… F. Bečvář,… M. Krtička et al., Physical Review C 84, (2011) 014306
[Do98] J. Dobeš, S. Pittel, Physical Review C 57 (1998) 688
[Gu11] M. Guttormsen, … M. Krtička et al., Physical Review C 83 (2011) 014312
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5. SCHEDULE AND BUDGET SPECIFICATIONS
Schedule: The duration of the project, 5 years, was chosen in view of the degree of intricacy
of the main research problems outlined above and due to the fact that processing of data from
experiments mentioned above takes several years. As some of experiments are only in the stage of
planning, there would be no possibility to achieve corresponding results earlier than in a horizon of
the planned duration of the project.
The work on various tasks under the specific subtopics (see Sec.2) will proceed in parallel, the
partial outputs to be continuously published in relevant international research journals. Based on our
experience from the previous years, the probable publication rate for the whole group is expected to
be about 7-10 journal papers and 4-7 conference contributions per year.
It is very difficult – especially for the theoretical work – to formulate an exact long-term
schedule of achievements: any fixed plan would have to be modified in view of the actual results.
Instead, we provide below a list of the main tasks in each part of the project for the first year: (a)
General outline and a preliminary analysis of the dynamical and entanglement effects of excitedstate phase transitions in the Lipkin and Dicke types of models (Subtopic A1). (b) Analysis of quantum
branch points in the complex-extended cusp model with first- and second-order QPTs (Subtopic A2).
(c) General SRPA analysis of the vorticity in heavy nuclei and the completion of computer programs
for microscopic many-body calculations within the equation-of-motion formalism in the j-coupled
scheme (subtopic B1). (d) Study of the M1 scissors mode in Gd, Tb and Lu nuclei – evaluation of
measurements from LANL and NPI Řež (Subtopic B2). (e) Analysis of random matrix ensembles with a
dominant diagonal and nearly Poissonian level statistics (Subtopic C1). (f) Search for consequences
and possible origins of the violation of the Porter-Thomas statistics in the decay of neutron
resonances and feasibility tests of measurements at GELINA facility (Subtopic C2). (g) Fourier analysis
of quantum spectra of the coupled-pendulum model and the use of the spectral lattice method for
generalized Hamiltonians of the interacting boson model (Subtopic C3).
Budget: Although experimental activities represent a rather important component of this
project, the financial requirements from the GAČR do not involve contributions to the experimental
equipment. Except of the personal expenses (i.e., the relevant parts of the salary and the associated
social insurance for individual members of the team), which represents approximately 62 % of the
budget, the required funding covers mainly the travelling expenses. These are connected with the
visits of the members of our team in the collaborating institutions abroad and the visits of foreign
experts in Prague (see the list of institutions and collaborating persons below the heading of each
subtopic in Sec.2). The possibility of an unmediated, joined work of the collaborating experts has a
vital importance for the progress in the above scientific program. We also intend to cover the
expenses connected with participation of our people in relevant conferences and workshops of the
respective fields. All together, the travelling expenses form about 15 % of the budget. About 3 % is
designed for the continuous upgrade of our computer facilities, software and information resources.
The remaining approx. 20 % of the required funding represents a contribution to the institutional
budget (as usual in the Czech Republic). The total amount needed is 3.85 million CZK per year.
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