92 research outputs found
Semiclassical scalar propagators in curved backgrounds: formalism and ambiguities
The phenomenology of quantum systems in curved space-times is among the most
fascinating fields of physics, allowing --often at the gedankenexperiment
level-- constraints on tentative theories of quantum gravity. Determining the
dynamics of fields in curved backgrounds remains however a complicated task
because of the highly intricate partial differential equations involved,
especially when the space metric exhibits no symmetry. In this article, we
provide --in a pedagogical way-- a general formalism to determine this dynamics
at the semiclassical order. To this purpose, a generic expression for the
semiclassical propagator is computed and the equation of motion for the
probability four-current is derived. Those results underline a direct analogy
between the computation of the propagator in general relativistic quantum
mechanics and the computation of the propagator for stationary systems in
non-relativistic quantum mechanics. A possible application of this formalism to
curvature-induced quantum interferences is also discussed.Comment: New materials on gravitationally-induced quantum interferences has
been adde
Semiclassical thermodynamics of scalar fields
We present a systematic semiclassical procedure to compute the partition
function for scalar field theories at finite temperature. The central objects
in our scheme are the solutions of the classical equations of motion in
imaginary time, with spatially independent boundary conditions. Field
fluctuations -- both field deviations around these classical solutions, and
fluctuations of the boundary value of the fields -- are resummed in a Gaussian
approximation. In our final expression for the partition function, this
resummation is reduced to solving certain ordinary differential equations.
Moreover, we show that it is renormalizable with the usual 1-loop counterterms.Comment: 24 pages, 5 postscript figure
Coherent states for a quantum particle on a circle
The coherent states for the quantum particle on the circle are introduced.
The Bargmann representation within the actual treatment provides the
representation of the algebra , where is unitary, which is a
direct consequence of the Heisenberg algebra , but it is
more adequate for the study of the circlular motion.Comment: 23 pages LaTeX, uses ioplppt.st
Path Integrals and Their Application to Dissipative Quantum Systems
Introduction
Path Integrals
- Introduction
- Propagator
- Free Particle
- Path Integral Representation of Quantum Mechanics
- Particle on a Ring
- Particle in a Box
- Driven Harmonic Oscillator
- Semiclassical Approximation
- Imaginary Time Path Integral
Dissipative Systems
- Introduction
- Environment as Collection of Harmonic Oscillators
- Effective Action
Damped Harmonic Oscillator
- Partition Function
- Ground State Energy and Density of States
- Position Autocorrelation FunctionComment: 55 pages, 13 figures. To be published in "Coherent Evolution in Noisy
Environments", Lecture Notes in Physics
(http://link.springer.de/series/lnpp/) (Springer Verlag,
Berlin-Heidelberg-New York
Quasi-classical path integral approach to supersymmetric quantum mechanics
{}From Feynman's path integral, we derive quasi-classical quantization rules
in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY
counterpart of Gutzwiller's formula, from which we obtain the quantization rule
of Comtet, Bandrauk and Campbell when SUSY is good. When SUSY is broken, we
arrive at a new quantization formula, which is found as good as and even
sometime better than the WKB formula in evaluating energy spectra for certain
one-dimensional bound state problems. The wave functions in the stationary
phase approximation are also derived for SUSY and broken SUSY cases. Insofar as
a broken SUSY case is concerned, there are strong indications that the new
quasi-classical approximation formula always overestimates the energy
eigenvalues while WKB always underestimates.Comment: 13 pages + 5 figures, complete paper submitted as postscript file, to
appear in Phys. Rev.
van Vleck determinants: geodesic focussing and defocussing in Lorentzian spacetimes
The van Vleck determinant is an ubiquitous object, arising in many physically
interesting situations such as: (1) WKB approximations to quantum time
evolution operators and Green functions. (2) Adiabatic approximations to heat
kernels. (3) One loop approximations to functional integrals. (4) The theory of
caustics in geometrical optics and ultrasonics. (5) The focussing and
defocussing of geodesic flows in Riemannian manifolds. While all of these
topics are interrelated, the present paper is particularly concerned with the
last case and presents extensive theoretical developments that aid in the
computation of the van Vleck determinant associated with geodesic flows in
Lorentzian spacetimes. {\sl A fortiori} these developments have important
implications for the entire array of topics indicated. PACS: 04.20.-q,
04.20.Cv, 04.60.+n. To appear in Physical Review D47 (1993) 15 March.Comment: plain LaTeX, 18 page
The next challenge for world wide robotized tele-echography experiment (WORTEX 2012): from engineering success to healthcare delivery.
Access to good quality healthcare remains difficult for many patients whether they live in developed or developing countries. In developed countries, specialist medical expertise is concentrated in major hospitals in urban settings both to improve clinical outcomes and as a strategy to reduce the costs of specialist healthcare delivery. In developing countries, millions of people have limited, if any, routine access to a healthcare system and due to economic and cultural factors the accessibility of any services may be restricted. In both cases, geographical, socio-political, cultural and economic factors produce ‘medically isolated areas’ where patients find themselves disadvantaged in terms of timely diagnosis and expert and/or expensive treatment. The robotized teleechography approach, also referred to as robotized teleultrasound, offers a potential solution to diagnostic imaging in medically isolated areas. It is designed for patients requiring ultrasound scans for routine care (e.g., ante natal care) and for diagnostic imaging to investigate acute and medical emergencies conditions, including trauma care and responses to natural disasters such as earthquakes. The robotized teleechography system can hold any standard ultrasound probe; this lightweight system is positioned on the patient’s body by a healthcare assistant. The medical expert, a clinician with expertise in ultrasound imaging and diagnosis, is in a distant location and, using a dedicated joystick, remotely controls the scanning via any available communication link (Internet, satellite). The WORTEX2012 intercontinental trials of the system conducted last year successfully demonstrated the feasibility of remote robotized tele-echography in a range of cultural, technical and clinical contexts. In addition to the engineering success, these trials provided positive feedback from the participating clinicians and patients on using the system and on the system’s perceived potential to transform healthcare in medically isolated areas. The next challenge is to show evidence that this innovative technology can deliver on its promise if introduced into routine healthcare
Phase Space Reduction and Vortex Statistics: An Anyon Quantization Ambiguity
We examine the quantization of the motion of two charged vortices in a
Ginzburg--Landau theory for the fractional quantum Hall effect recently
proposed by the first two authors. The system has two second-class constraints
which can be implemented either in the reduced phase space or
Dirac-Gupta-Bleuler formalism. Using the intrinsic formulation of statistics,
we show that these two ways of implementing the constraints are inequivalent
unless the vortices are quantized with conventional statistics; either
fermionic or bosonic.Comment: 14 pages, PHYZZ
Scaling, renormalization and statistical conservation laws in the Kraichnan model of turbulent advection
We present a systematic way to compute the scaling exponents of the structure
functions of the Kraichnan model of turbulent advection in a series of powers
of , adimensional coupling constant measuring the degree of roughness of
the advecting velocity field. We also investigate the relation between standard
and renormalization group improved perturbation theory. The aim is to shed
light on the relation between renormalization group methods and the statistical
conservation laws of the Kraichnan model, also known as zero modes.Comment: Latex (11pt) 43 pages, 22 figures (Feynman diagrams). The reader
interested in the technical details of the calculations presented in the
paper may want to visit:
http://www.math.helsinki.fi/mathphys/paolo_files/passive_scalar/passcal.htm
Particle detectors, geodesic motion, and the equivalence principle
It is shown that quantum particle detectors are not reliable probes of
spacetime structure. In particular, they fail to distinguish between inertial
and non-inertial motion in a general spacetime. To prove this, we consider
detectors undergoing circular motion in an arbitrary static spherically
symmetric spacetime, and give a necessary and sufficient condition for the
response function to vanish when the field is in the static vacuum state. By
examining two particular cases, we show that there is no relation, in general,
between the vanishing of the response function and the fact that the detector
motion is, or is not, geodesic. In static asymptotically flat spacetimes,
however, all rotating detectors are excited in the static vacuum. Thus, in this
particular case the static vacuum appears to be associated with a non-rotating
frame. The implications of these results for the equivalence principle are
considered. In particular, we discuss how to properly formulate the principle
for particle detectors, and show that it is satisfied.Comment: 14 pages. Revised version, with corrections; added two references.
Accepted for publication in Class. Quantum Gra
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