Species of spaces

• URL: http://arxiv.org/abs/2206.14603v2
• Date: Wed, 20 Jul 2022 08:19:54 GMT
• Title: Species of spaces
• Authors: Thierry Paul (LJLL)
• Abstract summary: The accent is put in situations where traces of noncommutativity, witness of an emblematic feature of quantum mechanise. Complex canonical transformations, spin-statistics, topological quantum fields theory, long time semiclassical approximation and underlying chaotic dynamics are considered.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of noncommutativity, witness of an emblematic feature of quantum mechanise remains when the Planck constant vanishes, in the framework of noncommutative geometry. Complex canonical transformations, spin-statistics, topological quantum fields theory, long time semiclassical approximation and underlying chaotic dynamics are considered, together with a comparison/fusion of classical unpredictability with quantum indeterminism.

Related papers

• The role of non-classicality in mediated spatial quantum correlations [0.0]
  The study of non-classicality is essential to understand the quantum-to-classical transition in physical systems. We propose a new inequality that quantitatively links the increase in quantum correlations between the probes to the degree of non-commutativity of the mediator's observables.
  arXiv  Detail & Related papers  (2024-10-01T16:07:04Z)
• Canonical description of quantum dynamics [0.0]
  This contribution presents various phase-space properties of moments describing a quantum state and its dynamics. An example of a geometrical reformulation of a non-classical quantum effect is given by an equivalence between conditions imposed by uncertainty relations and centrifugal barriers.
  arXiv  Detail & Related papers  (2023-01-12T16:47:32Z)
• Quantum Instability [30.674987397533997]
  We show how a time-independent, finite-dimensional quantum system can give rise to a linear instability corresponding to that in the classical system. An unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system.
  arXiv  Detail & Related papers  (2022-08-05T19:53:46Z)
• Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
  Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
  arXiv  Detail & Related papers  (2022-04-24T13:32:45Z)
• Random matrices: Application to quantum paradoxes [0.0]
  Recently, a geometric embedding of the classical space and classical phase space of an n-particle system was constructed and shown to be physically meaningful. Namely, the Newtonian dynamics of the particles was recovered from the Schroedinger dynamics by constraining the state of the system to the classical phase space submanifold of the space of states. A series of theorems related to the embedding and the Schroedinger evolution with a random Hamiltonian was proven and shown to be applicable to the process of measurement in classical and quantum mechanics.
  arXiv  Detail & Related papers  (2022-04-08T20:26:03Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Chaos in the quantum Duffing oscillator in the semiclassical regime under parametrized dissipation [0.0]
  We study the quantum dissipative Duffing oscillator across a range of system sizes and environmental couplings. We quantify the system sizes where quantum dynamics cannot be simulated using semiclassical or noise-added classical approximations. Our findings generalize the previous surprising result that classically regular orbits can have the greatest quantum-classical differences in the semiclassical regime.
  arXiv  Detail & Related papers  (2020-10-30T22:03:02Z)
• Quantum chaos in the spin coherent state representation [0.0]
  We use spin coherent states to compare classical and quantum evolution of a simple paradigmatic, discrete-time quantum dynamical system. In the paper, we presented a different way by comparing evolution of appropriately defined moments of classical and quantum distributions.
  arXiv  Detail & Related papers  (2020-10-27T15:04:40Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Emergence of classical behavior in the early universe [68.8204255655161]
  Three notions are often assumed to be essentially equivalent, representing different facets of the same phenomenon. We analyze them in general Friedmann-Lemaitre- Robertson-Walker space-times through the lens of geometric structures on the classical phase space. The analysis shows that: (i) inflation does not play an essential role; classical behavior can emerge much more generally; (ii) the three notions are conceptually distinct; classicality can emerge in one sense but not in another.
  arXiv  Detail & Related papers  (2020-04-22T16:38:25Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)

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.