Quantum behavior of a classical particle subject to a random force

• URL: http://arxiv.org/abs/2006.15995v2
• Date: Fri, 23 Oct 2020 06:54:21 GMT
• Title: Quantum behavior of a classical particle subject to a random force
• Authors: Can Gokler
• Abstract summary: We show that the Schrodinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the same result applies to small potential perturbations around the harmonic oscillator as long as the total potential preserves the periodicity of motion.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We give a partial answer to the question whether the Schrodinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one dimensional harmonic oscillator subject to a random force can be described by the Schrodinger equation for a period of time depending on the frequency and the energy of the oscillator. We achieve this by deriving the postulates of Nelson's stochastic formulation of quantum mechanics for a random force depending on a small parameter. We show that the same result applies to small potential perturbations around the harmonic oscillator as long as the total potential preserves the periodicity of motion with a small shift in frequency. We also show that the noise spectrum can be chosen to obtain the result for all oscillator frequencies for fixed mass. We discuss heuristics to generalize the result for a particle in one dimension in a potential where the motion can be described using action-angle variables.

Related papers

• Energetics of the dissipative quantum oscillator [22.76327908349951]
  We discuss some aspects of the energetics of a quantum Brownian particle placed in a harmonic trap. Based on the fluctuation-dissipation theorem, we analyze two distinct notions of thermally-averaged energy. We generalize our analysis to the case of the three-dimensional dissipative magneto-oscillator.
  arXiv  Detail & Related papers  (2023-10-05T15:18:56Z)
• Free expansion of a Gaussian wavepacket using operator manipulations [77.34726150561087]
  The free expansion of a Gaussian wavepacket is a problem commonly discussed in undergraduate quantum classes. We provide an alternative way to calculate the free expansion by recognizing that the Gaussian wavepacket can be thought of as the ground state of a harmonic oscillator. As quantum instruction evolves to include more quantum information science applications, reworking this well known problem using a squeezing formalism will help students develop intuition for how squeezed states are used in quantum sensing.
  arXiv  Detail & Related papers  (2023-04-28T19:20:52Z)
• Intrinsic quantum dynamics of particles in brane gravity [0.0]
  We show that the stability of particle trajectories on the brane gives us the Bohr--Sommerfeld quantization condition. The particle's motion along the extra dimension allows us to formulate a geometrical version of the uncertainty principle. We show that the particle's motion along the extra dimension yields a quantized energy spectrum for bound states.
  arXiv  Detail & Related papers  (2023-03-20T13:41:07Z)
• Quantum Uncertainty as an Intrinsic Clock [0.0]
  In quantum mechanics, a classical particle is raised to a wave-function, thereby acquiring many more degrees of freedom. We show that the Ermakov-Lewis invariant for the classical evolution in a time-dependent harmonic potential is actually the quantum uncertainty of a Gaussian wave-packet. This naturally extends the classical Ermakov-Lewis invariant to a constant of motion for quantum systems following Schrodinger equation.
  arXiv  Detail & Related papers  (2022-12-19T13:32:55Z)
• Schr\"odinger cat states of a 16-microgram mechanical oscillator [54.35850218188371]
  The superposition principle is one of the most fundamental principles of quantum mechanics. Here we demonstrate the preparation of a mechanical resonator with an effective mass of 16.2 micrograms in Schr"odinger cat states of motion. We show control over the size and phase of the superposition and investigate the decoherence dynamics of these states.
  arXiv  Detail & Related papers  (2022-11-01T13:29:44Z)
• The electrodynamic origin of the wave-particle duality [0.0]
  A derivation of pilot waves from electrodynamic self-interactions is presented. We abandon the current paradigm that describes electrodynamic bodies as point masses.
  arXiv  Detail & Related papers  (2022-10-14T09:27:47Z)
• Quantum vibrational mode in a cavity confining a massless spinor field [91.3755431537592]
  We analyse the reaction of a massless (1+1)-dimensional spinor field to the harmonic motion of one cavity wall. We demonstrate that the system is able to convert bosons into fermion pairs at the lowest perturbative order.
  arXiv  Detail & Related papers  (2022-09-12T08:21:12Z)
• Fall of a Particle to the Center of a Singular Potential: Classical vs. Quantum Exact Solutions [0.0]
  We inspect the quantum problem with the help of the conventional Schr"odinger's equation. Surprisingly, the quantum and classical solutions exhibit striking similarities.
  arXiv  Detail & Related papers  (2022-02-25T11:04:39Z)
• Equivalence of quantum harmonic oscillators and classical oscillators subject to random forces [0.0]
  We show that the Schr"odinger equation for the quantum harmonic oscillator can be derived as an approximation to the Newtonian mechanics. We generalize the Schr"odinger equation to non-interacting quantum harmonic oscillators.
  arXiv  Detail & Related papers  (2020-10-26T23:09:45Z)
• Zitterbewegung and Klein-tunneling phenomena for transient quantum waves [77.34726150561087]
  We show that the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit. We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront. The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime.
  arXiv  Detail & Related papers  (2020-03-09T21:27:02Z)
• External and internal wave functions: de Broglie's double-solution theory? [77.34726150561087]
  We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions. For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
  arXiv  Detail & Related papers  (2020-01-13T13:41:24Z)

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.