52 research outputs found
On the "Universal" N=2 Supersymmetry of Classical Mechanics
In this paper we continue the study of the geometrical features of a
functional approach to classical mechanics proposed some time ago. In
particular we try to shed some light on a N=2 "universal" supersymmetry which
seems to have an interesting interplay with the concept of ergodicity of the
system. To study the geometry better we make this susy local and clarify
pedagogically several issues present in the literature. Secondly, in order to
prepare the ground for a better understanding of its relation to ergodicity, we
study the system on constant energy surfaces. We find that the procedure of
constraining the system on these surfaces injects in it some local grassmannian
invariances and reduces the N=2 global susy to an N=1.Comment: few misprints fixed with respect to Int.Jour.Mod.Phys.A vol 16, no15
(2001) 270
On Epstein's trajectory model of non-relativistic quantum mechanics
In 1952 Bohm presented a theory about non-relativistic point-particles moving
along deterministic trajectories and showed how it reproduces the predictions
of standard quantum theory. This theory was actually presented before by de
Broglie in 1926, but Bohm's particular formulation of the theory inspired
Epstein to come up with a different trajectory model. The aim of this paper is
to examine the empirical predictions of this model. It is found that the
trajectories in this model are in general very different from those in the de
Broglie-Bohm theory. In certain cases they even seem bizarre and rather
unphysical. Nevertheless, it is argued that the model seems to reproduce the
predictions of standard quantum theory (just as the de Broglie-Bohm theory).Comment: 12 pages, no figures, LaTex; v2 minor improvement
The meeting problem in the quantum random walk
We study the motion of two non-interacting quantum particles performing a
random walk on a line and analyze the probability that the two particles are
detected at a particular position after a certain number of steps (meeting
problem). The results are compared to the corresponding classical problem and
differences are pointed out. Analytic formulas for the meeting probability and
its asymptotic behavior are derived. The decay of the meeting probability for
distinguishable particles is faster then in the classical case, but not
quadratically faster. Entangled initial states and the bosonic or fermionic
nature of the walkers are considered
Almost uniform sampling via quantum walks
Many classical randomized algorithms (e.g., approximation algorithms for
#P-complete problems) utilize the following random walk algorithm for {\em
almost uniform sampling} from a state space of cardinality : run a
symmetric ergodic Markov chain on for long enough to obtain a random
state from within total variation distance of the uniform
distribution over . The running time of this algorithm, the so-called {\em
mixing time} of , is , where
is the spectral gap of .
We present a natural quantum version of this algorithm based on repeated
measurements of the {\em quantum walk} . We show that it
samples almost uniformly from with logarithmic dependence on
just as the classical walk does; previously, no such
quantum walk algorithm was known. We then outline a framework for analyzing its
running time and formulate two plausible conjectures which together would imply
that it runs in time when is
the standard transition matrix of a constant-degree graph. We prove each
conjecture for a subclass of Cayley graphs.Comment: 13 pages; v2 added NSF grant info; v3 incorporated feedbac
Bell-Type Quantum Field Theories
In [Phys. Rep. 137, 49 (1986)] John S. Bell proposed how to associate
particle trajectories with a lattice quantum field theory, yielding what can be
regarded as a |Psi|^2-distributed Markov process on the appropriate
configuration space. A similar process can be defined in the continuum, for
more or less any regularized quantum field theory; such processes we call
Bell-type quantum field theories. We describe methods for explicitly
constructing these processes. These concern, in addition to the definition of
the Markov processes, the efficient calculation of jump rates, how to obtain
the process from the processes corresponding to the free and interaction
Hamiltonian alone, and how to obtain the free process from the free Hamiltonian
or, alternatively, from the one-particle process by a construction analogous to
"second quantization." As an example, we consider the process for a second
quantized Dirac field in an external electromagnetic field.Comment: 53 pages LaTeX, no figure
Quantum random walks with history dependence
We introduce a multi-coin discrete quantum random walk where the amplitude
for a coin flip depends upon previous tosses. Although the corresponding
classical random walk is unbiased, a bias can be introduced into the quantum
walk by varying the history dependence. By mixing the biased random walk with
an unbiased one, the direction of the bias can be reversed leading to a new
quantum version of Parrondo's paradox.Comment: 8 pages, 6 figures, RevTe
Fibre bundle formulation of nonrelativistic quantum mechanics: I. Introduction. The evolution transport
We propose a new systematic fibre bundle formulation of nonrelativistic
quantum mechanics. The new form of the theory is equivalent to the usual one
but it is in harmony with the modern trends in theoretical physics and
potentially admits new generalizations in different directions. In it a pure
state of some quantum system is described by a state section (along paths) of a
(Hilbert) fibre bundle. Its evolution is determined through the bundle
(analogue of the) Schr\"odinger equation. Now the dynamical variables and the
density operator are described via bundle morphisms (along paths). The
mentioned quantities are connected by a number of relations derived in this
work.
The present first part of this investigation is devoted to the introduction
of basic concepts on which the fibre bundle approach to quantum mechanics
rests. We show that the evolution of pure quantum-mechanical states can be
described as a suitable linear transport along paths, called evolution
transport, of the state sections in the Hilbert fibre bundle of states of a
considered quantum system.Comment: 26 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and
amsfonts are required. Revised: new material, references, and comments are
added. Minor style chages. Continuation of quan-ph/9803083. For continuation
of the this series see http://www.inrne.bas.bg/mathmod/bozhome
The still under-investigated role of cognitive deficits in PML diagnosis.
Background Despite cognitive deficits frequently represent the first clinical manifestations of Progressive Multifocal Leukoencephalopathy (PML) in Natalizumab-treated MS patients, the importance of cognitive deficits in PML diagnosis is still under-investigated. The aim of the current study is to investigate the cognitive deficits at PML diagnosis in a group of Italian patients with PML. Methods Thirty-four PML patients were included in the study. The demographic and clinical data, the lesion load and localization, and the longitudinal clinical course was compared between patients with (n = 13) and without (n = 15) cognitive deficit upon PML suspicion (the remaining six patients were asymptomatic). Clinical presentation of cognitive symptoms was described in detail. Result After symptoms detection, the time to diagnosis resulted to be shorter for patients presenting with cognitive than for patients with non cognitive onset (p = 0.03). Within patients with cognitive onset, six patients were presenting with language and/or reading difficulties (46.15%); five patients with memory difficulties (38.4%); three patients with apraxia (23.1%); two patients with disorientation (15.3%); two patients with neglect (15.3%); one patients with object agnosia (7.7%), one patient with perseveration (7.7%) and one patient with dementia (7.7%). Frontal lesions were less frequent (p = 0.03), whereas temporal lesions were slightly more frequent (p = 0.06) in patients with cognitive deficits. The longitudinal PML course seemed to be more severe in cognitive than in non cognitive patients (F = 2.73, p = 0.03), but differences disappeared (F = 1.24, p = 0.29) when balancing for the incidence of immune reconstitution syndrome and for other treatments for PML (steroids, plasma exchange (PLEX) and other therapies (Mefloquine, Mirtazapine, Maraviroc). Conclusion Cognitive deficits at PML onset manifest with symptoms which are absolutely rare in MS. Their appearance in MS patients should strongly suggest PML. Clinicians should be sensitive to the importance of formal neuropsychological evaluation, with particular focus on executive function, which are not easily detected without a formal assessment
- …