首页/论文/quant-ph/0509026

arXiv quant-ph/05090262005-09-03quant-ph

Particle dynamics in a relativistic invariant stochastic medium

Alejandro Cabo-Bizet, Alejandro Cabo Montes de Oca

备注：: 8 pages, 10 figures
DOI：: 10.1016/j.physleta.2006.06.047

英文摘要：

The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a function of the proper time of the particles. The equations of motion for a single one-dimensional particle are obtained and numerically solved. A conservation law for the drift momentum of the particle during its random motion is shown. Moreover, the conservation of the mean value of the total linear momentum for two particles repelling each other according with the Coulomb interaction is also following. Therefore, the results indicate the realization of a kind of stochastic Noether theorem in the system under study. Possible applications to the stochastic representation of Quantum Mechanics are advanced.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Relativistic and non-relativistic quantum Brownian motion in an anisotropic dissipative medium

Using a minimal-coupling-scheme we investigate the quantum Brownian motion of a particle in an anisotropic-dissipative-medium under the influence of an arbitrary potential in both relativistic and non-relativistic regimes. A general quantum Langevin equation is derived and explicit expressions for quantum-noise and dynamical variables of the system are obtained. The equations of motion for the canonical variables are solved explicitly and an expression for the radiation-reaction of a charged particle in the presence of a dissipative-medium is obtained. Some examples are given to elucidate the …

2014-01-30quant-ph

Relativistic Quantum Theory of Cyclotron Resonance in a Medium

In this paper the relativistic quantum theory of cyclotron resonance in an arbitrary medium is presented. The quantum equation of motion for charged particle in the field of plane electromagnetic wave and uniform magnetic field in a medium is solved in the eikonal approximation. The probabilities of induced multiphoton transitions between Landau levels in strong laser field is calculated.

2001-06-13quant-ph

A Canonical Relativistic Approach to Quantize Electromagnetic Field in the Presence of Moving Magneto-Dielectric Media

A canonical relativistic formulation is introduced to quantize electromagnetic field in the presence of a polarizable and magnetizable moving medium. The medium is modeled by a continuum of four vectors in a phenomenological way. The covariant wave equation for the vector potential and the covariant constitutive equation of the medium are obtained as the Euler- Lagrange equations using the Lagrangian of the total system. A tensor of the third rank which couples the electromagnetic field with the medium is introduced and the susceptibility tensor of the medium is obtained in terms of the coupli…

2009-08-08quant-ph

MARKOV DIFFUSIONS IN COMOVING COORDINATES AND STOCHASTIC QUANTIZATION OF THE FREE RELATIVISTIC SPINLESS PARTICLE

本文回顾了相对论流体力学中的经典同动坐标方法，并在适合于随机量子化的适当条件下，给出了它们的整体存在性的构造性证明。我们表明，它是可能的分配随机运动学的自由相对论性无自旋粒子作为一个马尔可夫扩散全球定义的${\sf M}^4$。然后利用随机变分原理引入动力学，得到Klein-Gordon方程的正能量解。该过程具有相对论协方差性质。

1995-05-16quant-ph

Exact Stochastic Reformulation of Non-Relativistic Quantum Dynamics

We show that any non-relativistic quantum N-body dynamics problem with pairwise interactions can be exactly reformulated in terms of N well behaved 1-body stochastic density equations. Specifically, the time evolving N-body density matrix is written as an average of tensor products of 1-body densities each of which obeys a stochastic evolution equation. Such decompositions can be constructed for any mixture of fermions and bosons. The evolution equations for the 1-body densities preserve norm, Hermiticity and positivity.

2004-07-05quant-ph

Finite temperature Cherenkov radiation in the presence of a magnetodielectric medium

A canonical approach to Cherenkov radiation in the presence of a magnetodielectric medium is presented in classical, nonrelativistic and relativistic quantum regimes. The equations of motion for the canonical variables are solved explicitly for both positive and negative times. Maxwell and related constitute equations are obtained. In the large-time limit, the vector potential operator is found and expressed in terms of the medium operators. The energy loss of a charged particle, emitted in the form of radiation, in finite temperature is calculated. A Dirac equation concerning the relativistic…

2010-09-15quant-ph

更多相关论文收起更多论文

Quantum Stochastics, Dirac Boundary Value Problem, and the Ultra Relativistic Limit

We prove that a single-jump quantum stochastic unitary evolution is equivalent to a Dirac boundary value problem on the half line in an extra dimension. This amounts to the equivalence of the quantum measurement boundary-value problem in infinite number particles space to the stochastic calculus in Fock space. It is shown that this exactly solvable model can be obtained from a Schroedinger boundary value problem for a positive relativistic Hamiltonian in the half-line as the inductive ultra relativistic limit, correspondent to the input flow of Dirac particles with asymptotically infinite mome…

2005-12-22quant-ph

On the stochastic mechanics of the free relativistic particle

Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time is an increasing stochastic process and we derive a probabilistic generalization of the equation $(dτ)^2=-\frac{1}{c^2}dX_νdX_ν$. A random time-change transformation provides the bridge between the $t$ and the $τ$ domain. In the $τ$ domain, we obtain an $\M^4$-valued Markov process with singular and constant diffusion coefficient. The square modulus of the K…

2001-08-31quant-ph

Simulation of the hydrogen ground state in Stochastic Electrodynamics-2: Inclusion of relativistic corrections

In a recent paper [arXiv:1502.06856] the authors studied numerically the hydrogen ground state in stochastic electrodynamics (SED) within the the non-relativistic approximation. In quantum theory the leading non-relativistic corrections to the ground state energy dominate the Lamb shift related to the photon cloud that should cause the quantum-like behaviour of SED. The present work takes these corrections into account in the numerical modelling. It is found that they have little effect; the self-ionisation that occurs without them remains present. It is speculated that the point-charge approx…

2016-11-10quant-ph

The Free Will Theorem, Stochastic Quantum Dynamics and True Becoming in Relativistic Quantum Physics

In Bell inequality tests, the evolution of the wavefunction is not covariant, i.e. not invariant under velocity boost that change the time ordering of events, but the laws that govern the probability distribution of possible results are. In this note I investigate what this could mean and whether there could be some covariant "real quantum stuff". This clarifies the implication of the Free Will Theorem and of relativistic spontaneous localization models based on the flash ontology (rGRWf). Some implications for the concept of time(s) are spelled out.

2010-02-06quant-ph

Stochastic Theory of Relativistic Quantum Mechanics

The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it also relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the classical trajectories of the particles are identical to the sample functions of a diffusion Markov process, whose conditional probability density is proposed as a substitute for the wave funct…

2020-06-07quant-ph

Stochastic particle annihilation: a model of state reduction in relativistic quantum field theory

A model of state reduction in relativistic quantum field theory involving a nonlinear stochastic extension of Schrödinger's equation is outlined. The eigenstates of the annihilation operator are chosen as the preferred basis onto which reduction occurs. These are the coherent states which saturate the bound of the Heisenberg uncertainty relation, exhibiting classical-like behavior. The quantum harmonic oscillator is studied in detail before generalizing to relativistic scalar quantum field theory. The infinite rates of increase in energy density which have plagued recent relativistic proposals…

2007-06-14quant-ph

Relativistic Brownian motion on a graphene chip

Relativistic Brownian motion can be inexpensively demonstrated on a graphene chip. The interplay of stochastic and relativistic dynamics, governing the transport of charge carrier in graphene, induces noise-controlled effects such as (i) a stochastic effective mass, detectable as a suppression of the particle mobility with increasing the temperature; (ii) a transverse ratchet effect, measurable as a net current orthogonal to an ac drive on an asymmetric substrate, and (iii) a chaotic stochastic resonance. Such properties can be of practical applications in the emerging graphene technology.

2012-02-28cond-mat.stat-mechquant-ph

Stochastic Quantization of Relativistic Theories

It was shown recently that stochastic quantization can be made into a well defined quantization scheme on (pseudo-)Riemannian manifolds using second order differential geometry, which is an extension of the commonly used first order differential geometry. In this letter, we show that restrictions to relativistic theories can be obtained from this theory by imposing a stochastic energy-momentum relation. In the process, we derive non-perturbative quantum corrections to the line element as measured by scalar particles. Furthermore, we extend the framework of stochastic quantization to massless s…

2021-11-10gr-qchep-thmath-ph

Mass spectrum from stochastic Levy-Schroedinger relativistic equations: possible qualitative predictions in QCD

Starting from the relation between the kinetic energy of a free Levy-Schroedinger particle and the logarithmic characteristic of the underlying stochastic process, we show that it is possible to get a precise relation between renormalizable field theories and a specific Levy process. This subsequently leads to a particular cut-off in the perturbative diagrams and can produce a phenomenological mass spectrum that allows an interpretation of quarks and leptons distributed in the three families of the standard model.

2011-11-12hep-phmath.PRquant-ph

Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method

A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-CDF (cumulative distribution function) method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to…

2022-04-27physics.chem-phphysics.comp-phquant-ph

Stochastic Theory of Relativistic Particles Moving in a Quantum Field: II. Scalar Abraham-Lorentz-Dirac-Langevin Equation, Radiation Reaction and Vacuum Fluctuations

We apply the open systems concept and the influence functional formalism introduced in Paper I to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the quantum and semi-classical captures the statistical mechanical attributes of the full theory. Applying the particle-centric world-line quantization formulation to the quantum field theory of scalar QED we derive a time-dependent (scalar) Abraham-Lorentz-Dirac (ALD) equation and show that it is the correct semiclassical limit for nonlinear particle-field syste…

2001-06-01gr-qchep-phquant-ph