106 research outputs found
Maximally Causal Quantum Mechanics
We present a new causal quantum mechanics in one and two dimensions developed
recently at TIFR by this author and V. Singh. In this theory both position and
momentum for a system point have Hamiltonian evolution in such a way that the
ensemble of system points leads to position and momentum probability densities
agreeing exactly with ordinary quantum mechanics.Comment: 7 pages,latex,no figures,to appear in Praman
Thermodynamic Gravity and the Schrodinger Equation
We adopt a 'thermodynamical' formulation of Mach's principle that the rest
mass of a particle in the Universe is a measure of its long-range collective
interactions with all other particles inside the horizon. We consider all
particles in the Universe as a 'gravitationally entangled' statistical ensemble
and apply the approach of classical statistical mechanics to it. It is shown
that both the Schrodinger equation and the Planck constant can be derived
within this Machian model of the universe. The appearance of probabilities,
complex wave functions, and quantization conditions is related to the
discreetness and finiteness of the Machian ensemble.Comment: Minor corrections, the version accepted by Int. J. Theor. Phy
Stationary Flows of the Parabolic Potential Barrier in Two Dimensions
In the two-dimensional isotropic parabolic potential barrier , though it is a model of an unstable system in quantum
mechanics, we can obtain the stationary states corresponding to the real energy
eigenvalue . Further, they are infinitely degenerate. For the first few
eigenstates, we will find the stationary flows round a right angle that are
expressed by the complex velocity potentials .Comment: 12 pages, AmS-LaTeX, 4 figure
Time-like flows of energy-momentum and particle trajectories for the Klein-Gordon equation
The Klein-Gordon equation is interpreted in the de Broglie-Bohm manner as a
single-particle relativistic quantum mechanical equation that defines unique
time-like particle trajectories. The particle trajectories are determined by
the conserved flow of the intrinsic energy density which can be derived from
the specification of the Klein-Gordon energy-momentum tensor in an
Einstein-Riemann space. The approach is illustrated by application to the
simple single-particle phenomena associated with square potentials.Comment: 14 pages, 11 figure
Justification of the symmetric damping model of the dynamical Casimir effect in a cavity with a semiconductor mirror
A "microscopic" justification of the "symmetric damping" model of a quantum
oscillator with time-dependent frequency and time-dependent damping is given.
This model is used to predict results of experiments on simulating the
dynamical Casimir effect in a cavity with a photo-excited semiconductor mirror.
It is shown that the most general bilinear time-dependent coupling of a
selected oscillator (field mode) to a bath of harmonic oscillators results in
two equal friction coefficients for the both quadratures, provided all the
coupling coefficients are proportional to a single arbitrary function of time
whose duration is much shorter than the periods of all oscillators. The choice
of coupling in the rotating wave approximation form leads to the "mimimum
noise" model of the quantum damped oscillator, introduced earlier in a pure
phenomenological way.Comment: 9 pages, typos corrected, corresponds to the published version,
except for the reference styl
Dirac-Hestenes spinor fields in Riemann-Cartan spacetime
In this paper we study Dirac-Hestenes spinor fields (DHSF) on a
four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields
must be defined as certain equivalence classes of even sections of the Clifford
bundle (over the RCST), thereby being certain particular sections of a new
bundle named Spin-Clifford bundle (SCB). The conditions for the existence of
the SCB are studied and are shown to be equivalent to the famous Geroch's
theorem concerning to the existence of spinor structures in a Lorentzian
spacetime. We introduce also the covariant and algebraic Dirac spinor fields
and compare these with DHSF, showing that all the three kinds of spinor fields
contain the same mathematical and physical information. We clarify also the
notion of (Crumeyrolle's) amorphous spinors (Dirac-K\"ahler spinor fields are
of this type), showing that they cannot be used to describe fermionic fields.
We develop a rigorous theory for the covariant derivatives of Clifford fields
(sections of the Clifford bundle (CB)) and of Dirac-Hestenes spinor fields. We
show how to generalize the original Dirac-Hestenes equation in Minkowski
spacetime for the case of a RCST. Our results are obtained from a variational
principle formulated through the multiform derivative approach to Lagrangian
field theory in the Clifford bundle.Comment: 45 pages, special macros kapproc.sty and makro822.te
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