2,319 research outputs found
Non-Unitary and Unitary Transitions in Generalized Quantum Mechanics, New Small Parameter and Information Problem Solving
Quantum Mechanics of the Early Universe is considered as deformation of a
well-known Quantum Mechanics. Similar to previous works of the author, the
principal approach is based on deformation of the density matrix with
concurrent development of the wave function deformation in the respective
Schr{\"o}dinger picture, the associated deformation parameter being interpreted
as a new small parameter. It is demonstrated that the existence of black holes
in the suggested approach in the end twice causes nonunitary transitions
resulting in the unitarity. In parallel this problem is considered in other
terms: entropy density, Heisenberg algebra deformation terms, respective
deformations of Statistical Mechanics, - all showing the identity of the basic
results. From this an explicit solution for Hawking's informaion paradox has
been derived.Comment: 18 page
The Universe as a Nonuniform Lattice in the Finite-Dimensional Hypercube II.Simple Cases of Symmetry Breakdown and Restoration
This paper continues a study of field theories specified for the nonuniform
lattice in the finite-dimensional hypercube with the use of the earlier
described deformation parameters. The paper is devoted to spontaneous breakdown
and restoration of symmetry in simple quantum-field theories with scalar
fields. It is demonstrated that an appropriate deformation opens up new
possibilities for symmetry breakdown and restoration. To illustrate, at low
energies it offers high-accuracy reproducibility of the same results as with a
nondeformed theory. In case of transition from low to higher energies and vice
versa it gives description for new types of symmetry breakdown and restoration
depending on the rate of the deformation parameter variation in time, and
indicates the critical points of the previously described lattice associated
with a symmetry restoration. Besides, such a deformation enables one to find
important constraints on the initial model parameters having an explicit
physical meaning.Comment: 9 pages,Revte
Pure States, Mixed States and Hawking Problem in Generalized Quantum Mechanics
This paper is the continuation of a study into the information paradox
problem started by the author in his earlier works. As previously, the key
instrument is a deformed density matrix in quantum mechanics of the early
universe. It is assumed that the latter represents quantum mechanics with
fundamental length. It is demonstrated that the obtained results agree well
with the canonical viewpoint that in the processes involving black holes pure
states go to the mixed ones in the assumption that all measurements are
performed by the observer in a well-known quantum mechanics. Also it is shown
that high entropy for Planck remnants of black holes appearing in the
assumption of the Generalized Uncertainty Relations may be explained within the
scope of the density matrix entropy introduced by the author previously. It is
noted that the suggested paradigm is consistent with the Holographic Principle.
Because of this, a conjecture is made about the possibility for obtaining the
Generalized Uncertainty Relations from the covariant entropy bound at high
energies in the same way as R. Bousso has derived Heisenberg uncertainty
principle for the flat space.Comment: 12 pages,no figures,some corrections,new reference
Quantum Mechanics at Planck's scale and Density Matrix
In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum
Mechanics at Planck's scale. This is possible due to the presence in the theory
of General Uncertainty Relations. Here Quantum Mechanics with Fundamental
Length is obtained as a deformation of Quantum Mechanics. The distinguishing
feature of the proposed approach in comparison with previous ones, lies on the
fact that here density matrix subjects to deformation whereas so far
commutators have been deformed. The density matrix obtained by deformation of
quantum-mechanical density one is named throughout this paper density
pro-matrix. Within our approach two main features of Quantum Mechanics are
conserved: the probabilistic interpretation of the theory and the well-known
measuring procedure corresponding to that interpretation. The proposed approach
allows to describe dynamics. In particular, the explicit form of deformed
Liouville's equation and the deformed Shr\"odinger's picture are given. Some
implications of obtained results are discussed. In particular, the problem of
singularity, the hypothesis of cosmic censorship, a possible improvement of the
definition of statistical entropy and the problem of information loss in black
holes are considered. It is shown that obtained results allow to deduce in a
simple and natural way the Bekenstein-Hawking's formula for black hole entropy
in semiclassical approximation.Comment: 18 pages,Latex,new reference
Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials
We consider an overdamped Brownian particle moving in a confining
asymptotically logarithmic potential, which supports a normalized Boltzmann
equilibrium density. We derive analytical expressions for the two-time
correlation function and the fluctuations of the time-averaged position of the
particle for large but finite times. We characterize the occurrence of aging
and nonergodic behavior as a function of the depth of the potential, and
support our predictions with extensive Langevin simulations. While the
Boltzmann measure is used to obtain stationary correlation functions, we show
how the non-normalizable infinite covariant density is related to the
super-aging behavior.Comment: 16 pages, 6 figure
Chow's theorem and universal holonomic quantum computation
A theorem from control theory relating the Lie algebra generated by vector
fields on a manifold to the controllability of the dynamical system is shown to
apply to Holonomic Quantum Computation. Conditions for deriving the holonomy
algebra are presented by taking covariant derivatives of the curvature
associated to a non-Abelian gauge connection. When applied to the Optical
Holonomic Computer, these conditions determine that the holonomy group of the
two-qubit interaction model contains . In particular, a
universal two-qubit logic gate is attainable for this model.Comment: 13 page
Different frequencies of RIP among early vs. late ascospores of Neurospora crassa
We have noticed that the frequency of RIP can be quite variable, even in crosses of the same strains. One possible source of variability is the time at which ascospores are harvested. We reasoned that the earliest ascospores shot from a perithecium might contain DNA that went through relatively few mitotic divisions in pre-meiosis. RIP occurs between fertilization and premeiotic DNA synthesis (Selker et al. 1987 Cell 51:741-752). Thus, early spores might have less exposure to RIP than late spores. Since all ascospores from a perithecium are thought to arise from a single fertilization event, a minimum of 7- 10 divisions are required to account for the number of ascospores normally produced (Perkins and Barry, 1977 Adv. Genet. 211:541-544). It is likely, however, that some ascospore lineages contain fewer divisions than others
Geometric Control Over the Motion of Magnetic Domain Walls
We propose a method, which enables precise control of magnetic patterns,
relying only on the fundamental properties of the wire and the choice of the
path in the controlled parameter space but not on the rate of motion along this
path. Possible experimental realizations of this mechanism are discussed. In
particular, we show that the domain walls in magnetic nanowires can be
translated by rotation of the magnetic easy axis, or by applying pulses of
magnetic field directed transverse to the magnetic easy axis.Comment: 4 pages, 4 figure
On distributions of functionals of anomalous diffusion paths
Functionals of Brownian motion have diverse applications in physics,
mathematics, and other fields. The probability density function (PDF) of
Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger
equation in imaginary time. In recent years there is a growing interest in
particular functionals of non-Brownian motion, or anomalous diffusion, but no
equation existed for their PDF. Here, we derive a fractional generalization of
the Feynman-Kac equation for functionals of anomalous paths based on
sub-diffusive continuous-time random walk. We also derive a backward equation
and a generalization to Levy flights. Solutions are presented for a wide number
of applications including the occupation time in half space and in an interval,
the first passage time, the maximal displacement, and the hitting probability.
We briefly discuss other fractional Schrodinger equations that recently
appeared in the literature.Comment: 25 pages, 4 figure
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