Quantum theory, thermal gradients and the curved Euclidean space

• URL: http://arxiv.org/abs/2206.13324v1
• Date: Mon, 27 Jun 2022 14:10:09 GMT
• Title: Quantum theory, thermal gradients and the curved Euclidean space
• Authors: S. Ganesh
• Abstract summary: We develop an equivalence between the spatial variation of temperature in a thermal bath and the curvature of the Euclidean space. The equivalence is substantiated by analyzing the Polyakov loop, the partition function and the periodicity of the correlation function. The Dirac equation for an external Dirac spinor, traversing in a thermal bath with spatial thermal gradients, is solved in the curved Euclidean space.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Euclidean space, obtained by the analytical continuation of time, to an imaginary time, is used to model thermal systems. In this work, it is taken a step further to systems with spatial thermal variation, by developing an equivalence between the spatial variation of temperature in a thermal bath and the curvature of the Euclidean space. The variation in temperature is recast as a variation in the metric, leading to a curved Euclidean space. The equivalence is substantiated by analyzing the Polyakov loop, the partition function and the periodicity of the correlation function. The bulk thermodynamic properties like the energy, entropy and the Helmholtz free energy are calculated from the partition function, for small metric perturbations, for a neutral scalar field. The Dirac equation for an external Dirac spinor, traversing in a thermal bath with spatial thermal gradients, is solved in the curved Euclidean space. The fundamental behavior exhibited by the Dirac spinor eigenstate, may provide a possible mechanism to validate the theory, at a more basal level, than examining only bulk thermodynamic properties. Furthermore, in order to verify the equivalence at the level of classical mechanics, the geodesic equation is analyzed in a classical backdrop. The mathematical apparatus is borrowed from the physics of quantum theory in a gravity-induced space-time curvature. As spatial thermal variations are obtainable at QCD or QED energies, it may be feasible for the proposed formulation to be validated experimentally.

Related papers

• The temperature dependent thermal potential in Quantum Boltzmann equation [0.0]
  We express the thermal scalar and vector potential by the distribution function in damping force, which originates from the scattering of conduction electrons. The influence from quantum correction terms in QBE are also considered, which contribute not only to the damping force, but also to the anomalous velocity in the drift term.
  arXiv  Detail & Related papers  (2024-10-02T09:19:10Z)
• Quantum stochastic thermodynamics: A semiclassical theory in phase space [0.0]
  A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space. We use a Fokker-Planck equation as the dynamics at the mesoscopic level. We define thermodynamic quantities based on the trajectories of the phase-space distribution.
  arXiv  Detail & Related papers  (2023-03-10T14:12:14Z)
• Quantum kinetic theory of nonlinear thermal current [1.4174475093445236]
  We develop the quantum kinetic theory framework to describe thermal transport in presence of a temperature gradient. We show that the intrinsic thermal current is determined by the band geometric quantities and is non-zero in systems where both the space inversion and time-reversal symmetries are broken.
  arXiv  Detail & Related papers  (2022-11-03T15:28:11Z)
• Boundary-induced singularity in strongly-correlated quantum systems at finite temperature [2.2451981098432516]
  We study the bulk-boundary competition in a simulative Hamiltonian, with which the thermodynamic properties of the infinite-size translationally-invariant system can be optimally mimicked. Our results show that such a singularity differs from those in the conventional thermodynamic phase transition points that normally fall into the Landau-Ginzburg paradigm.
  arXiv  Detail & Related papers  (2022-04-14T08:30:30Z)
• 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)
• Fast Thermalization from the Eigenstate Thermalization Hypothesis [69.68937033275746]
  Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state. Our results explain finite-time thermalization in chaotic open quantum systems.
  arXiv  Detail & Related papers  (2021-12-14T18:48:31Z)
• Breakdown of quantum-classical correspondence and dynamical generation of entanglement [6.167267225728292]
  We study the generation of quantum entanglement induced by an ideal Fermi gas confined in a chaotic cavity. We find that the breakdown of the quantum-classical correspondence of particle motion, via dramatically changing the spatial structure of many-body wavefunction, leads to profound changes of the entanglement structure.
  arXiv  Detail & Related papers  (2021-04-14T03:09:24Z)
• 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)
• 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)
• Out-of-equilibrium quantum thermodynamics in the Bloch sphere: temperature and internal entropy production [68.8204255655161]
  An explicit expression for the temperature of an open two-level quantum system is obtained. This temperature coincides with the environment temperature if the system reaches thermal equilibrium with a heat reservoir. We show that within this theoretical framework the total entropy production can be partitioned into two contributions.
  arXiv  Detail & Related papers  (2020-04-09T23:06:43Z)

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.