377 research outputs found
Non-Markovian Effects on the Brownian Motion of a Free Particle
Non-Markovian effects upon the Brownian movement of a free particle in the
presence as well as in the absence of inertial force are investigated within
the framework of Fokker-Planck equations (Rayleigh and Smoluchowski equations).
More specifically, it is predicted that non-Markovian features can enhance the
values of the mean square displacement and momentum, thereby assuring the
mathematical property of differentiability of the these physically observable
quantities
How to prepare quantum states that follow classical paths
We present an alternative quantization procedure for the one-dimensional
non-relativistic quantum mechanics. We show that, for the case of a free
particle and a particle in a box, the complete classical and quantum
correspondence can be obtained using this formulation. The resulting wave
packets do not disperse and strongly peak on the classical paths. Moreover, for
the case of the free particle, they satisfy minimum uncertainty relation.Comment: 10 pages, 3 figures, to appear in Europhysics Letter
Wigner phase space distribution as a wave function
We demonstrate that the Wigner function of a pure quantum state is a wave
function in a specially tuned Dirac bra-ket formalism and argue that the Wigner
function is in fact a probability amplitude for the quantum particle to be at a
certain point of the classical phase space. Additionally, we establish that in
the classical limit, the Wigner function transforms into a classical
Koopman-von Neumann wave function rather than into a classical probability
distribution. Since probability amplitude need not be positive, our findings
provide an alternative outlook on the Wigner function's negativity.Comment: 6 pages and 2 figure
Effective gravity from a quantum gauge theory in Euclidean space-time
We consider a gauge theory in an Euclidean -dimensional
space-time, which is known to be renormalizable to all orders in perturbation
theory for . Then, with the help of a space-time representation of
the gauge group, the gauge theory is mapped into a curved space-time with
linear connection. Further, in that mapping the gauge field plays the role of
the linear connection of the curved space-time and an effective metric tensor
arises naturally from the mapping. The obtained action, being quadratic in the
Riemann-Christoffel tensor, at a first sight, spoils a gravity interpretation
of the model. Thus, we provide a sketch of a mechanism that breaks the
color invariance and generates the Einstein-Hilbert term, as well as a
cosmological constant term, allowing an interpretation of the model as a
modified gravity in the Palatini formalism. In that sense, gravity can be
visualized as an effective classical theory, originated from a well defined
quantum gauge theory. We also show that, in the four dimensional case, two
possibilities for particular solutions of the field equations are the de Sitter
and Anti de Sitter space-times.Comment: 20 pages; Final version accepted for publication in Class.Quant.Gra
Operational Dynamic Modeling Transcending Quantum and Classical Mechanics
We introduce a general and systematic theoretical framework for Operational
Dynamic Modeling (ODM) by combining a kinematic description of a model with the
evolution of the dynamical average values. The kinematics includes the algebra
of the observables and their defined averages. The evolution of the average
values is drawn in the form of Ehrenfest-like theorems. We show that ODM is
capable of encompassing wide ranging dynamics from classical non-relativistic
mechanics to quantum field theory. The generality of ODM should provide a basis
for formulating novel theories.Comment: 23 pages and 2 figures. Sec. VII B "Phase Space Representation in
Curvilinear Coordinates" was correcte
- …