Related papers: A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics

A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics

URL: http://arxiv.org/abs/2410.20531v1
Date: Sun, 27 Oct 2024 17:53:08 GMT
Title: A Path Integral Treatment of Time-dependent Dunkl Quantum Mechanics
Authors: A. Benchikha, B. Hamil, B. C. Lütfüoğlu,
Abstract summary: We reformulated the path integral to develop an explicit expression for the propagator. This formalism is applied to specific cases, including a Dunkl-harmonic oscillator with time-dependent mass and frequency.
Score: 0.0
License:
Abstract: This paper presents an analytical treatment of the path integral formalism for time-dependent quantum systems within the framework of Wigner-Dunkl mechanics, emphasizing systems with varying masses and time-dependent potentials. By employing generalized canonical transformations, we reformulated the path integral to develop an explicit expression for the propagator. This formalism is applied to specific cases, including a Dunkl-harmonic oscillator with time-dependent mass and frequency. Solutions for the Dunkl-Caldirola-Kanai oscillator and a model with a strongly pulsating mass are derived, providing exact propagator expressions and corresponding wave functions. These findings extend the utility of Dunkl operators in quantum mechanics, offering new insights into the dynamics of time-dependent quantum systems.

Related papers

Time-dependent Dunkl-Pauli Oscillator [0.0]
We construct the Dunkl-Pauli Hamiltonian, which incorporates a time-varying magnetic field and a harmonic oscillator characterized by time-dependent mass and frequency. Our findings regarding the total quantum phase factor and wave functions reveal the significant impact of Dunkl operators on quantum systems.
arXiv Detail & Related papers (2024-10-24T07:38:02Z)
Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential [0.0]
The Schr"odinger equation is a fundamental equation in quantum mechanics. Over the past decade, theoretical studies have focused on adapting the Dunkl derivative to quantum mechanical problems.
arXiv Detail & Related papers (2024-08-04T13:11:52Z)
Schwinger-Keldysh path integral formalism for a Quenched Quantum Inverted Oscillator [0.0]
We study the time-dependent behaviour of quantum correlations of a system governed by out-of-equilibrium dynamics. Next, we study a specific case, where the system exhibits chaotic behaviour by computing the quantum Lyapunov from the time-dependent behaviour of OTOC.
arXiv Detail & Related papers (2022-10-03T18:00:02Z)
Free to Harmonic Unitary Transformations in Quantum and Koopman Dynamics [0.0]
We show that an equivalent transformation can be performed for classical systems in the context of Koopman von-Neumann (KvN) dynamics. We further extend this mapping to dissipative evolutions in both the quantum and classical cases, and show that this mapping imparts an identical time-dependent scaling on the dissipation parameters for both types of dynamics.
arXiv Detail & Related papers (2022-07-19T18:59:01Z)
Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
arXiv Detail & Related papers (2022-02-15T19:00:09Z)
From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
arXiv Detail & Related papers (2021-07-29T18:27:38Z)
On the Problem of Time(s) in Quantum Mechanics and Quantum Gravity: recent integrating developments and outlook [0.0]
How to restore time is the Problem of Time(s) It introduces an intrinsic time property tau associated with the mass of the system. It invalidates Pauli's objection to the existence of a time operator.
arXiv Detail & Related papers (2021-04-20T17:51:05Z)
Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
arXiv Detail & Related papers (2021-02-18T20:55:04Z)
Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
arXiv Detail & Related papers (2021-02-08T14:55:44Z)
Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
arXiv Detail & Related papers (2021-01-21T22:18:49Z)
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)

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