66 research outputs found
Towards nonlinear quantum Fokker-Planck equations
It is demonstrated how the equilibrium semiclassical approach of Coffey et
al. can be improved to describe more correctly the evolution. As a result a new
semiclassical Klein-Kramers equation for the Wigner function is derived, which
remains quantum for a free quantum Brownian particle as well. It is transformed
to a semiclassical Smoluchowski equation, which leads to our semiclassical
generalization of the classical Einstein law of Brownian motion derived before.
A possibility is discussed how to extend these semiclassical equations to
nonlinear quantum Fokker-Planck equations based on the Fisher information
Quantum noise in current biased Josephson junction
Quantum fluctuations in a current biased Josephson junction, described in
terms of the RCSJ-model, are considered. The fluctuations of the voltage and
phase across the junction are assumed to be initiated by equilibrium current
fluctuations in the shunting resistor. This corresponds to low enough
temperatures, when fluctuations of the normal current in the junction itself
can be neglected. We used the quantum Langevin equation in terms of random
variables related to the limit cycle of the nonlinear Josephson oscillator.
This allows to go beyond the perturbation theory and calculate the widths of
the Josephson radiation lines
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
Corrections to Einstein's relation for Brownian motion in a tilted periodic potential
In this paper we revisit the problem of Brownian motion in a tilted periodic
potential. We use homogenization theory to derive general formulas for the
effective velocity and the effective diffusion tensor that are valid for
arbitrary tilts. Furthermore, we obtain power series expansions for the
velocity and the diffusion coefficient as functions of the external forcing.
Thus, we provide systematic corrections to Einstein's formula and to linear
response theory. Our theoretical results are supported by extensive numerical
simulations. For our numerical experiments we use a novel spectral numerical
method that leads to a very efficient and accurate calculation of the effective
velocity and the effective diffusion tensor.Comment: 29 pages, 7 figures, submitted to the Journal of Statistical Physic
Fluctuations and Dissipation of Coherent Magnetization
A quantum mechanical model is used to derive a generalized Landau-Lifshitz
equation for a magnetic moment, including fluctuations and dissipation. The
model reproduces the Gilbert-Brown form of the equation in the classical limit.
The magnetic moment is linearly coupled to a reservoir of bosonic degrees of
freedom. Use of generalized coherent states makes the semiclassical limit more
transparent within a path-integral formulation. A general
fluctuation-dissipation theorem is derived. The magnitude of the magnetic
moment also fluctuates beyond the Gaussian approximation. We discuss how the
approximate stochastic description of the thermal field follows from our
result. As an example, we go beyond the linear-response method and show how the
thermal fluctuations become anisotropy-dependent even in the uniaxial case.Comment: 22 page
Enhancement of the magnetic anisotropy of nanometer-sized Co clusters: influence of the surface and of the inter-particle interactions
We study the magnetic properties of spherical Co clusters with diameters
between 0.8 nm and 5.4 nm (25 to 7500$ atoms) prepared by sequential sputtering
of Co and Al2O3. The particle size distribution has been determined from the
equilibrium susceptibility and magnetization data and it is compared to
previous structural characterizations. The distribution of activation energies
was independently obtained from a scaling plot of the ac susceptibility.
Combining these two distributions we have accurately determined the effective
anisotropy constant Keff. We find that Keff is enhanced with respect to the
bulk value and that it is dominated by a strong anisotropy induced at the
surface of the clusters. Interactions between the magnetic moments of adjacent
layers are shown to increase the effective activation energy barrier for the
reversal of the magnetic moments. Finally, this reversal is shown to proceed
classically down to the lowest temperature investigated (1.8 K).Comment: 13 figures submitted to Phys. Rev.
Fractional Fokker-Planck equation for anomalous diffusion in a potential: Exact matrix continued fraction solutions
Methods for the exact solution of fractional Fokker-Planck equations for anomalous diffusion in an external potential are discussed using both ordinary and matrix continued fractions, whereby the scalar multi-term recurrence relations generated by such fractional diffusion equations are reduced to three-term matrix ones. The procedure is illustrated by solving various problems concerning the anomalous translational diffusion in both periodic and double-well potentials
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