A Stochastic Origin of Spacetime Non-Commutativity

• URL: http://arxiv.org/abs/2409.11866v2
• Date: Tue, 10 Dec 2024 09:09:30 GMT
• Title: A Stochastic Origin of Spacetime Non-Commutativity
• Abstract summary: We discuss how the (non-)commutativity of spacetime is inherently related to the continuity or discontinuity of paths in the path integral formulation.<n>Our findings suggest that spacetime non-commutativity can be understood as a result of fundamental discreteness in temporal and/or spatial evolution.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a stochastic interpretation of spacetime non-commutativity starting from the path integral formulation of quantum mechanical commutation relations. We discuss how the (non-)commutativity of spacetime is inherently related to the continuity or discontinuity of paths in the path integral formulation. Utilizing Wiener processes, we demonstrate that continuous paths lead to commutative spacetime, whereas discontinuous paths correspond to non-commutative spacetime structures. As an example we introduce discontinuous paths from which the $\kappa$-Minkowski spacetime commutators can be obtained. Moreover we focus on modifications of the Leibniz rule for differentials acting on discontinuous trajectories. We show how these can be related to the deformed action of translation generators focusing, as a working example, on the $\kappa$-Poincar\'e algebra. Our findings suggest that spacetime non-commutativity can be understood as a result of fundamental discreteness in temporal and/or spatial evolution.

Related papers

• Stochastic Counterdiabatic Driving via Biorthogonal Liouvillian Eigenmodes [42.668742604089324]
  Escorted free energy simulations address the non-adiabatic lag by engineering control fields $mathbfu$ that eliminate the lag.<n>We construct a complementary numerical framework based on gauge-type transforms instead of generalized coordinate transforms.<n>We show that the counterdiabatic condition is satisfied to machine precision, with the non-adiabatic lag suppressed by roughly twelve orders of magnitude.
  arXiv  Detail & Related papers  (2026-07-27T13:08:14Z)
• Path integral formulation of finite-dimensional quantum mechanics in discrete phase space [0.0]
  We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space.<n>For Hamiltonians linear in the phase-space coordinates, we show that the fluctuation sum factorizes.<n>We show explicitly that the full entanglement dynamics requires the coherent contribution of all fluctuation sectors of the action.
  arXiv  Detail & Related papers  (2026-04-22T17:04:10Z)
• Forward and inverse problems for measure flows in Bayes Hilbert spaces [10.897369732123844]
  We study forward and inverse problems for time-dependent probability measures in Bayes--Hilbert spaces.<n>We prove existence of minimizers, derive first-variation formulas, establish local stability of the observation map, and deduce recovery of the evolving law.
  arXiv  Detail & Related papers  (2026-03-20T04:01:41Z)
• Nonlinearity-Inhomogeneity Competition in Discrete-Time Quantum Walks [0.0]
  We investigate the interplay between nonlinearity and inhomogeneities in discrete-time quantum walks on one-dimensional lattices.<n> Spatial inhomogeneities weaken nonlinear self-trapping and constrict the region of robust localization.<n> temporal inhomogeneities act as time-dependent perturbations that disrupt the phase coherence required for self-trapped excitation.
  arXiv  Detail & Related papers  (2026-02-25T01:03:57Z)
• Continuum Limits of Lazy Open Quantum Walks [0.04297070083645049]
  We derive the continuous spacetime limit of the one dimensional lazy discrete time quantum walk.<n>We show that the unitary limit is governed by a Dirac-type SU(3) Hamiltonian describing ballistic advection of left and right moving modes.
  arXiv  Detail & Related papers  (2025-12-19T16:28:26Z)
• Tailoring transport in quantum spin chains via disorder and collisions [41.94295877935867]
  We investigate the interplay of disorder and time-homogeneous collisional noise in shaping the transport dynamics of anisotropic XXZZ spin chain.<n>We find that space-homogeneous and low-rate collisions can shape regions where localization sets in the form of subsequent plateaus.<n>Our findings can be applied to design stroboscopic protocols where sequences of transport and localization can be tailored.
  arXiv  Detail & Related papers  (2025-02-21T15:11:58Z)
• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• Radiative transport in a periodic structure with band crossings [47.82887393172228]
  We derive the semi-classical model for the Schr"odinger equation in arbitrary spatial dimensions. We consider both deterministic and random scenarios. As a specific application, we deduce the effective dynamics of a wave packet in graphene with randomness.
  arXiv  Detail & Related papers  (2024-02-09T23:34:32Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• On the path integral simulation of space-time fractional Schroedinger equation with time independent potentials [0.0]
  A Feynman-Kac path integral method has been proposed for solving the Cauchy problems associated with the space-time fractional Schroedinger equations. We have been able to simulate the space-time fractional diffusion process with comparable simplicity and convergence rate as in the case of a standard diffusion.
  arXiv  Detail & Related papers  (2023-06-25T20:14:40Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
  The percolation transition is defined through the appearance of the infinite cluster. We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient. Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
  arXiv  Detail & Related papers  (2022-10-15T13:53:21Z)
• Tunable Non-equilibrium Phase Transitions between Spatial and Temporal Order through Dissipation [3.190771753066767]
  We propose an experiment with a driven quantum gas coupled to a dissipative cavity that realizes a far-from-equilibrium phase transition between spatial and temporal order. For negative detunings, the system features a spatially ordered phase, while positive detunings lead to a phase with both spatial order and persistent oscillations, which we call dissipative-temporal lattice. In both the atoms are subject to an accelerated transport, either via a uniform acceleration or via abrupt transitions to higher momentum states.
  arXiv  Detail & Related papers  (2022-05-03T12:52:11Z)
• Relativistic Extended Uncertainty Principle from Spacetime Curvature [0.0]
  Investigation directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. Applying the 3+1-splitting in accordance with the ADM-formalism, we find the relativistic physical momentum operator and compute its standard deviation for wave functions confined to a geodesic ball on a spacelike hypersurface.
  arXiv  Detail & Related papers  (2021-11-30T17:21:49Z)
• Particle in uniform field in noncommutative space with preserved time reversal and rotational symmetries [0.0]
  We find exactly the energy of a particle in uniform field in the quantized space and its wavefunctions. It is shown that the motion of the particle in the field direction in time reversal invariant and rotationally invariant noncommutative space is the same as in the ordinary space.
  arXiv  Detail & Related papers  (2021-02-19T16:10:05Z)
• The Connection between Discrete- and Continuous-Time Descriptions of Gaussian Continuous Processes [60.35125735474386]
  We show that discretizations yielding consistent estimators have the property of invariance under coarse-graining' This result explains why combining differencing schemes for derivatives reconstruction and local-in-time inference approaches does not work for time series analysis of second or higher order differential equations.
  arXiv  Detail & Related papers  (2021-01-16T17:11:02Z)
• New approach to describe two coupled spins in a variable magnetic field [55.41644538483948]
  We describe the evolution of two spins coupled by hyperfine interaction in an external time-dependent magnetic field. We modify the time-dependent Schr"odinger equation through a change of representation. The solution is highly simplified when an adiabatically varying magnetic field perturbs the system.
  arXiv  Detail & Related papers  (2020-11-23T17:29:31Z)
• Nonlinear entanglement growth in inhomogeneous spacetimes [0.0]
  Entment has become central for the characterization of quantum matter both in and out of equilibrium. We study entanglement dynamics both for the case of noninteracting fermions, allowing for exact numerical solutions, and for random unitary circuits representing a paradigmatic class of ergodic systems.
  arXiv  Detail & Related papers  (2020-06-01T08:58:26Z)
• Projection evolution and quantum spacetime [68.8204255655161]
  We discuss the problem of time in quantum mechanics. An idea of construction of a quantum spacetime as a special set of the allowed states is presented. An example of a structureless quantum Minkowski-like spacetime is also considered.
  arXiv  Detail & Related papers  (2019-10-24T14:54:11Z)

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.