The generalized Schrödinger–Langevin equation

Journal Article · Tue Jul 15 04:00:00 EDT 2014 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2014.04.004· OSTI ID:22314833

Bargueño, Pedro ^[1]; Miret-Artés, Salvador ^[2]

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1. Departamento de Física, Universidad de los Andes, Apartado Aéreo 4976, Bogotá, Distrito Capital (Colombia)
2. Instituto de Física Fundamental, CSIC, Serrano 123, 28006, Madrid (Spain)

In this work, for a Brownian particle interacting with a heat bath, we derive a generalization of the so-called Schrödinger–Langevin or Kostin equation. This generalization is based on a nonlinear interaction model providing a state-dependent dissipation process exhibiting multiplicative noise. Two straightforward applications to the measurement process are then analyzed, continuous and weak measurements in terms of the quantum Bohmian trajectory formalism. Finally, it is also shown that the generalized uncertainty principle, which appears in some approaches to quantum gravity, can be expressed in terms of this generalized equation. -- Highlights: •We generalize the Kostin equation for arbitrary system–bath coupling. •This generalization is developed both in the Schrödinger and Bohmian formalisms. •We write the generalized Kostin equation for two measurement problems. •We reformulate the generalized uncertainty principle in terms of this equation.

• OSTI ID: 22314833
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: Complete Vol. 346; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BROWNIAN MOVEMENT
COUPLING
LANGEVIN EQUATION
NOISE
NONLINEAR PROBLEMS
QUANTUM GRAVITY
QUANTUM MECHANICS
SCHROEDINGER EQUATION
UNCERTAINTY PRINCIPLE