Wigner functions in quantum mechanics with a minimum length scale arising from generalized uncertainty principle

• URL: http://arxiv.org/abs/2006.11582v2
• Date: Wed, 27 Jan 2021 17:04:21 GMT
• Title: Wigner functions in quantum mechanics with a minimum length scale arising from generalized uncertainty principle
• Authors: Prathamesh Yeole, Vipul Kumar, Kaushik Bhattacharya
• Abstract summary: We generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale. We show that the Weyl transform and the Wigner function does satisfy some of their known properties in standard quantum mechanics.
• Score: 1.4502611532302039
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper we generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale arising due to the application of a generalized uncertainty principle (GUP). We present the phase space formulation of such theories following GUP and show that the Weyl transform and the Wigner function does satisfy some of their known properties in standard quantum mechanics. We utilise the generalized Wigner function to calculate the phase space average of the Hamiltonian of a quantum harmonic oscillator satisfying deformed Heisenberg algebra. It is also shown that averages of certain quantum mechanical operators in such theories may restrict the value of the deformation parameter specifying the degree of deformation of Heisenberg algebra. All the results presented are for pure states. The results can be generalized for mixed states.

Related papers

• Phase-space gaussian ensemble quantum camouflage [0.0]
  We extend the phase-space description of the Weyl-Wigner quantum mechanics to a subset of non-linear Hamiltonians in position and momentum. For gaussian statistical ensembles, the exact phase-space profile of the quantum fluctuations over the classical trajectories are found.
  arXiv  Detail & Related papers  (2024-09-24T18:14:07Z)
• Summation formulas generated by Hilbert space eigenproblem [0.0]
  We show that certain classes of Schl" omilch-like infinite series and series can be calculated in closed form. We provide a general framework based on the Hilbert space eigenproblem that can be applied to different exactly solvable quantum models.
  arXiv  Detail & Related papers  (2023-10-26T07:55:05Z)
• Quantum tomography of helicity states for general scattering processes [55.2480439325792]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• On the gravitization of quantum mechanics and wave function reduction in Bohmian quantum mechanics [0.0]
  This paper uses Einstein's equivalence principle in the description of the gravity-induced wave function reduction in the framework of Bohmian causal quantum theory. The critical mass for transition from the quantum world to the classical world, the reduction time of the wave function and the temperature that corresponds to the Unruh temperature will be obtained.
  arXiv  Detail & Related papers  (2022-09-01T14:58:35Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Holomorphic representation of quantum computations [0.0]
  We study bosonic quantum computations using the Segal-Bargmann representation of quantum states. We argue that this holomorphic representation is a natural one which gives a canonical description of bosonic quantum computing.
  arXiv  Detail & Related papers  (2021-10-29T23:26:51Z)
• Generalized Uncertainty Principle: from the harmonic oscillator to a QFT toy model [0.0]
  We modify the Heisenberg Uncertainty Principle into the Generalized Uncertainty Principle. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. We construct a quantum field theoretic toy model based on the Generalized Uncertainty Principle.
  arXiv  Detail & Related papers  (2021-09-30T16:55:48Z)
• Experimental Validation of Fully Quantum Fluctuation Theorems Using Dynamic Bayesian Networks [48.7576911714538]
  Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. We experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup.
  arXiv  Detail & Related papers  (2020-12-11T12:55:17Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

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.