11,453 research outputs found
Kinetic energy of a free quantum Brownian particle
We consider a paradigmatic model of a quantum Brownian particle coupled to a thermostat
consisting of harmonic oscillators. In the framework of a generalized Langevin equation, the memory
(damping) kernel is assumed to be in the form of exponentially-decaying oscillations. We discuss
a quantum counterpart of the equipartition energy theorem for a free Brownian particle in a thermal
equilibrium state. We conclude that the average kinetic energy of the Brownian particle is equal to
thermally-averaged kinetic energy per one degree of freedom of oscillators of the environment,
additionally averaged over all possible oscillators’ frequencies distributed according to some
probability density in which details of the particle-environment interaction are present via the
parameters of the damping kernel
Noise perturbations in the Brownian motion and quantum dynamics
The third Newton law for mean velocity fields is utilised to generate
anomalous (enhanced) or non-dispersive diffusion-type processes which, in
particular, can be interpreted as a probabilistic counterpart of the
Schr\"{o}dinger picture quantum dynamics.Comment: Phys. Lett. A, (1999), in pres
Quantum features derived from the classical model of a bouncer-walker coupled to a zero-point field
In our bouncer-walker model a quantum is a nonequilibrium steady-state
maintained by a permanent throughput of energy. Specifically, we consider a
"particle" as a bouncer whose oscillations are phase-locked with those of the
energy-momentum reservoir of the zero-point field (ZPF), and we combine this
with the random-walk model of the walker, again driven by the ZPF. Starting
with this classical toy model of the bouncer-walker we were able to derive
fundamental elements of quantum theory. Here this toy model is revisited with
special emphasis on the mechanism of emergence. Especially the derivation of
the total energy hbar.omega and the coupling to the ZPF are clarified. For this
we make use of a sub-quantum equipartition theorem. It can further be shown
that the couplings of both bouncer and walker to the ZPF are identical. Then we
follow this path in accordance with previous work, expanding the view from the
particle in its rest frame to a particle in motion. The basic features of
ballistic diffusion are derived, especially the diffusion constant D, thus
providing a missing link between the different approaches of our previous
works.Comment: 14 pages, based on a talk given at "Emergent Quantum Mechanics (Heinz
von Foerster Conference 2011)", see
http://www.univie.ac.at/hvf11/congress/EmerQuM.htm
A classical explanation of quantization
In the context of our recently developed emergent quantum mechanics, and, in
particular, based on an assumed sub-quantum thermodynamics, the necessity of
energy quantization as originally postulated by Max Planck is explained by
means of purely classical physics. Moreover, under the same premises, also the
energy spectrum of the quantum mechanical harmonic oscillator is derived.
Essentially, Planck's constant h is shown to be indicative of a particle's
"zitterbewegung" and thus of a fundamental angular momentum. The latter is
identified with quantum mechanical spin, a residue of which is thus present
even in the non-relativistic Schroedinger theory.Comment: 20 pages; version accepted for publication in Foundations of Physic
Vacuum fluctuations of a scalar field near a reflecting boundary and their effects on the motion of a test particle
The contribution from quantum vacuum fluctuations of a real massless scalar
field to the motion of a test particle that interacts with the field in the
presence of a perfectly reflecting flat boundary is here investigated. There is
no quantum induced dispersions on the motion of the particle when it is alone
in the empty space. However, when a reflecting wall is introduced, dispersions
occur with magnitude dependent on how fast the system evolves between the two
scenarios. A possible way of implementing this process would be by means of an
idealized sudden switching, for which the transition occurs instantaneously.
Although the sudden process is a simple and mathematically convenient
idealization it brings some divergences to the results, particularly at a time
corresponding to a round trip of a light signal between the particle and the
wall. It is shown that the use of smooth switching functions, besides
regularizing such divergences, enables us to better understand the behavior of
the quantum dispersions induced on the motion of the particle. Furthermore, the
action of modifying the vacuum state of the system leads to a change in the
particle energy that depends on how fast the transition between these states is
implemented. Possible implications of these results to the similar case of an
electric charge near a perfectly conducting wall are discussed.Comment: 17 pages, 8 figure
Quantum optical versus quantum Brownian motion master-equation in terms of covariance and equilibrium properties
Structures of quantum Fokker-Planck equations are characterized with respect
to the properties of complete positivity, covariance under symmetry
transformations and satisfaction of equipartition, referring to recent
mathematical work on structures of unbounded generators of covariant quantum
dynamical semigroups. In particular the quantum optical master-equation and the
quantum Brownian motion master-equation are shown to be associated to
and symmetry respectively. Considering the motion
of a Brownian particle, where the expression of the quantum Fokker-Planck
equation is not completely fixed by the aforementioned requirements, a recently
introduced microphysical kinetic model is briefly recalled, where a quantum
generalization of the linear Boltzmann equation in the small energy and
momentum transfer limit straightforwardly leads to quantum Brownian motion.Comment: 11 pages, latex, no figures, slight changes and a few references
added, to appear in J. Math. Phy
Nonlinear theory of quantum Brownian motion
A nonlinear theory of quantum Brownian motion in classical environment is
developed based on a thermodynamically enhanced nonlinear Schrodinger equation.
The latter is transformed via the Madelung transformation into a nonlinear
quantum Smoluchowski-like equation, which is proven to reproduce key results
from quantum and classical physics. The application of the theory to a free
quantum Brownian particle results in a nonlinear dependence of the position
dispersion on time, being quantum generalization of the Einstein law of
Brownian motion. It is shown that the time of decoherence for the transition
from quantum to classical diffusion is proportional to the square of the
thermal de Broglie wavelength divided by the Einstein diffusion constant
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