• Corpus ID: 208513337

Time in quantum mechanics: A fresh look on quantum hydrodynamics and quantum trajectories

@article{Schild2019TimeIQ,
  title={Time in quantum mechanics: A fresh look on quantum hydrodynamics and quantum trajectories},
  author={Axel Schild},
  journal={arXiv: Quantum Physics},
  year={2019}
}
  • A. Schild
  • Published 29 November 2019
  • Physics
  • arXiv: Quantum Physics
Quantum hydrodynamics is a formulation of quantum mechanics based on the probability density and flux (current) density of a quantum system. It can be used to define trajectories which allow for a particle-based interpretation of quantum mechanics, commonly known as Bohmian mechanics. However, quantum hydrodynamics rests on the usual time-dependent formulation of quantum mechanics where time appears as a parameter. This parameter describes the correlation of the state of the quantum system with… 

Figures from this paper

The Augmented Jump Chain -- a sparse representation of time-dependent Markov jump processes
TLDR
A representation of non-autonomous Markov jump processes as autonomous Markov chains on space-time is presented and the so-called augmented jump chain is derived, which provides a useful tool for studying time-dependent dynamics even in high dimensions.

References

SHOWING 1-10 OF 85 REFERENCES
Dynamics in the quantum/classical limit based on selective use of the quantum potential.
TLDR
A hybrid approach is used to examine evolution of light/heavy systems in the harmonic and double-well potentials, using conventional grid-based and approximate quantum-trajectory time propagation.
Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory
Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schrödinger's equation into a completely coherent physical theory. It describes a world in which particles move in a
Equivalent emergence of time dependence in classical and quantum mechanics
Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when
Quantum equilibrium and the origin of absolute uncertainty
The quantum formalism is a “measurement” formalism-a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from
Time in quantum mechanics: A fresh look at the continuity equation
The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with
Time dependence in quantum mechanics
Abstract:It is shown that the time-dependent equations (Schrödinger and Dirac) for a quantum system can be derived from the time-independent equation for the larger object of the system interacting
Quantum Hydrodynamics
Quantum plasma physics is a rapidly evolving research field with a very inter-disciplinary scope of potential applications, ranging from nano-scale science in condensed matter to the vast scales of
Classical limit of the interaction of a quantum system with the electromagnetic field
The interaction of nonrelativistic matter with the quantized electromagnetic field is investigated in the classical limit of large photon numbers. Quantization of both matter, say an atom, and the
The time as an emergent property of quantum mechanics, a synthetic description of a first experimental approach
The ’’problem of time” in present physics substantially consists in the fact that a straightforward quantization of the general relativistic evolution equation and constraints generates for the
Electronic transitions with quantum trajectories. II
The quantum trajectory method (QTM) is applied to nonadiabatic electronic transitions. Equations of motion in a Lagrangian framework are derived for the probability density, velocity, position, and
...
...