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

Quantum systems with a finite number of freedom degrees f develop robust singularities in the energy spectrum of excited states as the system’s size increases to infinity. We analyze the general form of these singularities for low f, particularly f=2, clarifying the relation to classical stationary points of the corresponding potential. Signatures in the smoothed energy dependence of the quantum state density and in the flow of energy levels with an arbitrary control parameter are described along with the relevant thermodynamical consequences. The general analysis is illustrated with specific examples of excited-state singularities accompanying the first-order quantum phase transition. -- Highlights: •ESQPTs found in infinite-size limit of systems with low numbers of freedom degrees f. •ESQPTs related to non-analytical evolutions of classical phase–space properties. •ESQPT signatures analyzed for general f, particularly f=2, extending known case f=1. •ESQPT signatures identified in smoothened density and flow of energy spectrum. •ESQPTs shown to induce a new type of thermodynamic anomalies.
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [1]
  1. Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000 Prague (Czech Republic)
  2. (Mexico)
  3. Racah Institute of Physics, The Hebrew University, 91904 Jerusalem (Israel)
  4. (Czech Republic)
Publication Date:
OSTI Identifier:
22314821
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 345; Journal Issue: Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DEGREES OF FREEDOM; ENERGY DEPENDENCE; ENERGY SPECTRA; ENERGY-LEVEL DENSITY; EXCITED STATES; PHASE SPACE; PHASE TRANSFORMATIONS; POTENTIALS; QUANTUM STATES; SINGULARITY; THERMODYNAMIC PROPERTIES