Excited-state quantum phase transitions in systems with two degrees of freedom: Level density, level dynamics, thermal properties

Stránský, Pavel; Macek, Michal; Cejnar, Pavel

doi:10.1016/j.aop.2014.03.006

Cited by 113 publications

(203 citation statements)

References 29 publications

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“…Analytical expressions for its eigenenergies have been reported [26][27][28][29][30]. Another important feature in the Hamiltonian is the excited-state quantum phase transitions (ESQPT) [31,32], manifested as a singularity in the level density, order parameters, and wave function properties [33,34]. They could have important effects in decoherence [35] and in the temporal evolution for quantum quenches [36].…”

Section: Arxiv:150905918v1 [Quant-ph] 19 Sep 2015mentioning

confidence: 99%

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Delocalization and quantum chaos in atom-field systems

et al. 2016

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Employing efficient diagonalization techniques, we perform a detailed quantitative study of the regular and chaotic regions in phase space in the simplest non-integrable atom-field system, the Dicke model. A close correlation between the classical Lyapunov exponents and the quantum Participation Ratio of coherent states on the eigenenergy basis is exhibited for different points in the phase space. It is also shown that the Participation Ratio scales linearly with the number of atoms in chaotic regions, and with its square root in the regular ones.

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Section: Arxiv:150905918v1 [Quant-ph] 19 Sep 2015mentioning

confidence: 99%

“…They are marked by the ESQPT [13,34,46], sudden changes in the slope of the density of states. For energies in the interval ∈ [ 0 (γ), −ω 0 ] the surface of constant energy is formed by two disconnected lobes, which merges as the energy reaches = −ω 0 .…”

Section: B the Classical Hamiltonianmentioning

confidence: 99%

Delocalization and quantum chaos in atom-field systems

et al. 2016

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“…More recently, considerable attention has been given to the so-called excited-state quantum phase transition (ESQPT) [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Unlike GSQPT, an ESQPT can occur not only with variation of the control parameters of a model Hamiltonian, but also with the increasing of the excitation energy.…”

Section: Introductionmentioning

confidence: 99%

Excited-state quantum phase transitions in the interacting boson model: Spectral characteristics of0+states and effective order parameter

2016

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The spectral characteristics of the L π = 0 + excited-states in the interacting boson model are systematically investigated. It is found that various types of excited-state quantum phase transitions may widely occur in the model as functions of the excitation energy, which indicates that the phase diagram of the interacting boson model can be dynamically extended along the direction of the excitation energy. It has also been justified that the d-boson occupation probability ρ(E) is qualified to be taken as the effective order parameter to identify these excited-state quantum phase transitions. In addition, the underlying relation between the excite-state quantum phase transition and the chaotic dynamics is also stated.

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“…On the contrary, the density of states for models with more than one semiclassical degree of freedom is not singular. In these cases, the logarithmic singularity occurs in its derivative ρ (E) [37]. This feature has been tested in the integrable Tavis-Cummings model with one semiclassical degree of freedom, and in the nonintegrable Dicke model with two semiclassical degrees of freedom [17].…”

Section: Excited-state Quantum Phase Transitionsmentioning

confidence: 99%

“…Traditionally, ESQPTs have been linked to singularities in the density of states or in one of its derivatives, depending on the number of system's degrees of freedom in the semiclassical limit [37]. It has been shown that for a system with just one effective degree of freedom, as the Tavis-Cummings model, a λ singularity in the density of states characterizes the ESQPT.…”

Section: Excited-state Quantum Phase Transitionsmentioning

confidence: 99%

Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential

et al. 2014

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The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: (i) an interacting atomic Bose gas, and (ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground state is degenerate. For repulsive and small attractive interaction, the ground state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition. In both cases, a critical energy separates a region in which all the energy levels are degenerate in pairs, from another region in which there are no degeneracies. For the atomic system, the critical point displays a singularity in the density of states, whereas this behavior is largely smoothed for the mixed atom-molecule system.

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Excited-state quantum phase transitions in systems with two degrees of freedom: Level density, level dynamics, thermal properties

Cited by 113 publications

References 29 publications

Delocalization and quantum chaos in atom-field systems

Delocalization and quantum chaos in atom-field systems

Excited-state quantum phase transitions in the interacting boson model: Spectral characteristics of0+states and effective order parameter

Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential

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