56 research outputs found
Lie-Algebraic Characterization of 2D (Super-)Integrable Models
It is pointed out that affine Lie algebras appear to be the natural
mathematical structure underlying the notion of integrability for
two-dimensional systems. Their role in the construction and classification of
2D integrable systems is discussed. The super- symmetric case will be
particularly enphasized. The fundamental examples will be outlined.Comment: 6 pages, LaTex, Talk given at the conference in memory of D.V.
Volkov, Kharkhov, January 1997. To appear in the proceeding
Bayesian Probabilities and the Histories Algebra
We attempt a justification of a generalisation of the consistent histories
programme using a notion of probability that is valid for all complete sets of
history propositions. This consists of introducing Cox's axioms of probability
theory and showing that our candidate notion of probability obeys them. We also
give a generalisation of Bayes' theorem and comment upon how Bayesianism should
be useful for the quantum gravity/cosmology programmes.Comment: 10 pages, accepted by Int. J. Theo. Phys. Feb 200
Influence Action and decoherence of hydrodynamic modes
We derive an influence action for the heat diffusion equation and from its
spectral dependence show that long wavelength hydrodynamic modes are most
readily decohered. The result is independent of the details of the microscopic
dynamics, and follows from general principles alone.Comment: 5 pages, no figure
Classicality of quantum information processing
The ultimate goal of the classicality programme is to quantify the amount of
quantumness of certain processes. Here, classicality is studied for a
restricted type of process: quantum information processing (QIP). Under special
conditions, one can force some qubits of a quantum computer into a classical
state without affecting the outcome of the computation. The minimal set of
conditions is described and its structure is studied. Some implications of this
formalism are the increase of noise robustness, a proof of the quantumness of
mixed state quantum computing and a step forward in understanding the very
foundation of QIP.Comment: Minor changes, published in Phys. Rev. A 65, 42319 (2002
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
Decoherence : An irreversible Process
A wide-ranging theory of decoherence is derived from the quantum theory of
irreversible processes, with specific results having for their main limitation
the assumption of an exact pointer basis.Comment: 9 page
Comparing Formulations of Generalized Quantum Mechanics for Reparametrization-Invariant Systems
A class of decoherence schemes is described for implementing the principles
of generalized quantum theory in reparametrization-invariant `hyperbolic'
models such as minisuperspace quantum cosmology. The connection with
sum-over-histories constructions is exhibited and the physical equivalence or
inequivalence of different such schemes is analyzed. The discussion focuses on
comparing constructions based on the Klein-Gordon product with those based on
the induced (a.k.a. Rieffel, Refined Algebraic, Group Averaging, or Spectral
Analysis) inner product. It is shown that the Klein-Gordon and induced products
can be simply related for the models of interest. This fact is then used to
establish isomorphisms between certain decoherence schemes based on these
products.Comment: 21 pages ReVTe
Partial waves of baryon-antibaryon in three-body B meson decay
The conspicuous threshold enhancement has been observed in the
baryon-antibaryon subchannels of many three-body B decay modes. By examining
the partial waves of baryon-antibaryon, we first show for B- -->pp-bar K- that
the pK- angular correlation rules out dominance of a single pp-bar partial wave
for the enhancement, for instance, the resonance hypothesis or the strong
final-state interaction in a single channel. The measured pK- angular
correlation turns out to be opposite to the naive expectation of the
short-distance picture. We study the origin of this reversed angular
correlation in the context of the pp-bar partial waves and argue that NN-bar
bound states may be the cause of this sign reversal. Dependence of the angular
correlation on the pp-bar invariant mass is very important to probe the
underlying problem from the experimental side.Comment: 16 pages, 9 figures, the version for journal publicatio
Time-of-arrival probabilities for general particle detectors
We develop a general framework for the construction of probabilities for the
time of arrival in quantum systems. The time of arrival is identified with the
time instant when a transition in the detector's degrees of freedom takes
place. Thus, its definition is embedded within the larger issue of defining
probabilities with respect to time for general quantum transitions. The key
point in our analysis is that we manage to reduce the problem of defining a
quantum time observable to a mathematical model where time is associated to a
transition from a subspace of the Hilbert space of the total system to its
complementary subspace. This property makes it possible to derive a general
expression for the probability for the time of transition, valid for any
quantum system, with the only requirement that the time of transition is
correlated with a definite macroscopic record.
The framework developed here allows for the consideration of any experimental
configuration for the measurement of the time of arrival and it also applies to
relativistic systems with interactions described by quantum field theory. We
use the method in order to describe time-of-arrival measurements in high-energy
particle reactions and for a rigorous derivation of the time-integrated
probabilities in particle oscillations.Comment: 27 pages, latex. Changed title and added a conclusions section.
Version to appear in PR
Stochastic Theory of Relativistic Particles Moving in a Quantum Field: II. Scalar Abraham-Lorentz-Dirac-Langevin Equation, Radiation Reaction and Vacuum Fluctuations
We apply the open systems concept and the influence functional formalism
introduced in Paper I to establish a stochastic theory of relativistic moving
spinless particles in a quantum scalar field. The stochastic regime resting
between the quantum and semi-classical captures the statistical mechanical
attributes of the full theory. Applying the particle-centric world-line
quantization formulation to the quantum field theory of scalar QED we derive a
time-dependent (scalar) Abraham-Lorentz-Dirac (ALD) equation and show that it
is the correct semiclassical limit for nonlinear particle-field systems without
the need of making the dipole or non-relativistic approximations. Progressing
to the stochastic regime, we derive multiparticle ALD-Langevin equations for
nonlinearly coupled particle-field systems. With these equations we show how to
address time-dependent dissipation/noise/renormalization in the semiclassical
and stochastic limits of QED. We clarify the the relation of radiation
reaction, quantum dissipation and vacuum fluctuations and the role that initial
conditions may play in producing non-Lorentz invariant noise. We emphasize the
fundamental role of decoherence in reaching the semiclassical limit, which also
suggests the correct way to think about the issues of runaway solutions and
preacceleration from the presence of third derivative terms in the ALD
equation. We show that the semiclassical self-consistent solutions obtained in
this way are ``paradox'' and pathology free both technically and conceptually.
This self-consistent treatment serves as a new platform for investigations into
problems related to relativistic moving charges.Comment: RevTex; 20 pages, 3 figures, Replaced version has corrected typos,
slightly modified derivation, improved discussion including new section with
comparisons to related work, and expanded reference
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