Improved models for ideal Fermi gas and ideal Bose gas using quantum phase space

• URL: http://arxiv.org/abs/2407.09998v3
• Date: Sat, 21 Sep 2024 14:43:32 GMT
• Title: Improved models for ideal Fermi gas and ideal Bose gas using quantum phase space
• Authors: Rivo Herivola Manjakamanana Ravelonjato, Ravo Tokiniaina Ranaivoson, Raoelina Andriambololona, Roland Raboanary, Naivo Rabesiranana, Solofoarisina Wilfrid Chrysante,
• Abstract summary: It is shown that the improvements can be introduced into the current models of ideal Fermi and ideal gas. The construction of the improved models is based on the use of the concepts of phase space representation of quantum mechanics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, it is shown that the improvements can be introduced into the current models of ideal Fermi and ideal gas to take into account the quantum nature of phase space related to the uncertainty principle. The construction of the improved models is based on the use of the concepts of phase space representation of quantum mechanics and quantum phase space that were introduced and developed recently. Hamiltonian operator of a gas particle and its eigenstates are firstly determined and the use of quantum statistical mechanics leads to the deduction of the thermodynamics properties of the ideal gas itself. The explicit expressions of thermodynamic quantities such as the grand canonical potential, the thermodynamic particles number, the internal energy, the Von Neumann entropy and the pressure as well as the state equations, corresponding to the improved models, are established for both bosons and fermions. The corrections introduced by these expressions are expected to be particularly significant at low temperature and for confined volume. They permit in particular to highlight the existence of quantum shape and size effects. It is also shown that the thermodynamics functions and variables are directly related to the momenta quantum statistical variances. Well-known relations corresponding to classical ideal gas model can be retrieved from the improved models as asymptotic limits at high temperature and for large volume.

Related papers

• Thermalization and Criticality on an Analog-Digital Quantum Simulator [133.58336306417294]
  We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions. We digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization.
  arXiv  Detail & Related papers  (2024-05-27T17:40:39Z)
• Analytic thermodynamic properties of the Lieb-Liniger gas [0.0]
  We present a review on the state-of-the-art of the approximate analytic approaches describing the finite-temperature thermodynamic quantities of the Lieb-Liniger model of the 1D Bose gas. This paradigmatic model of quantum many-body-theory plays an important role in many areas of physics.
  arXiv  Detail & Related papers  (2024-04-09T07:50:05Z)
• Signatures of a quantum phase transition on a single-mode bosonic model [0.0]
  Equilibrium phase transitions emerge from the microscopic behavior of many-body systems. They can be defined through the non-analytic behavior of thermodynamic potentials in the thermodynamic limit. Taking previous ideas to the extreme, we argue that such a limit can be defined even in non-extended systems.
  arXiv  Detail & Related papers  (2023-03-22T20:14:45Z)
• Quantum and Relativistic corrections to Maxwell-Boltzmann ideal gas model from a Quantum Phase Space approach [0.0]
  It is shown that the corrections in the non-relativistic quantum case may be particularly useful to describe the deviation from classical behavior of a Maxwell-Boltzmann gas at low temperature and in confined space. For the relativistic quantum case, the corrections could be relevant for confined space and when the thermal energy of each particle is comparable to their rest energy.
  arXiv  Detail & Related papers  (2023-02-18T15:05:48Z)
• Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines [0.0]
  We show that the standard approach of equilibrium physics can be extended to the slow driving regime in a thermodynamically consistent way. We use a Lindblad-type quantum master equation to work out a dynamical model of a quantum many-body engine using a harmonically trapped Bose gas. Our work paves the way for a more general thermodynamic framework that makes it possible to systematically assess the impact of quantum many-body effects on the performance of thermal machines.
  arXiv  Detail & Related papers  (2022-12-22T23:14:00Z)
• Gauge Quantum Thermodynamics of Time-local non-Markovian Evolutions [77.34726150561087]
  We deal with a generic time-local non-Markovian master equation. We define current and power to be process-dependent as in classical thermodynamics. Applying the theory to quantum thermal engines, we show that gauge transformations can change the machine efficiency.
  arXiv  Detail & Related papers  (2022-04-06T17:59:15Z)
• Entropy Production and the Role of Correlations in Quantum Brownian Motion [77.34726150561087]
  We perform a study on quantum entropy production, different kinds of correlations, and their interplay in the driven Caldeira-Leggett model of quantum Brownian motion.
  arXiv  Detail & Related papers  (2021-08-05T13:11:05Z)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)
• Analog cosmological reheating in an ultracold Bose gas [58.720142291102135]
  We quantum-simulate the reheating-like dynamics of a generic cosmological single-field model in an ultracold Bose gas. Expanding spacetime as well as the background oscillating inflaton field are mimicked in the non-relativistic limit. The proposed experiment has the potential of exploring the evolution up to late times even beyond the weak coupling regime.
  arXiv  Detail & Related papers  (2020-08-05T18:00:26Z)
• Quantum corrections to the entropy in a driven quantum Brownian motion model [2.28438857884398]
  We study the von Neumann entropy of a particle undergoing quantum Brownian motion. Our results bring important insights to the understanding of entropy in open quantum systems.
  arXiv  Detail & Related papers  (2020-08-05T14:13:39Z)
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
  The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
  arXiv  Detail & Related papers  (2020-07-20T18:00:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.