673 research outputs found
Phase transitions and quantum measurements
In a quantum measurement, a coupling between the system S and the
apparatus A triggers the establishment of correlations, which provide
statistical information about S. Robust registration requires A to be
macroscopic, and a dynamical symmetry breaking of A governed by S allows the
absence of any bias. Phase transitions are thus a paradigm for quantum
measurement apparatuses, with the order parameter as pointer variable. The
coupling behaves as the source of symmetry breaking. The exact solution of
a model where S is a single spin and A a magnetic dot (consisting of
interacting spins and a phonon thermal bath) exhibits the reduction of the
state as a relaxation process of the off-diagonal elements of S+A, rapid due to
the large size of . The registration of the diagonal elements involves a
slower relaxation from the initial paramagnetic state of A to either one of its
ferromagnetic states. If is too weak, the measurement fails due to a
``Buridan's ass'' effect. The probability distribution for the magnetization
then develops not one but two narrow peaks at the ferromagnetic values. During
its evolution it goes through wide shapes extending between these values.Comment: 12 pages, 2 figure
The Quantum Measurement Process: Lessons from an Exactly Solvable Model
The measurement of a spin-\half is modeled by coupling it to an apparatus,
that consists of an Ising magnetic dot coupled to a phonon bath. Features of
quantum measurements are derived from the dynamical solution of the
measurement, regarded as a process of quantum statistical mechanics.
Schr\"odinger cat terms involving both the system and the apparatus, die out
very quickly, while the registration is a process taking the apparatus from its
initially metastable state to one of its stable final states. The occurrence of
Born probabilities can be inferred at the macroscopic level, by looking at the
pointer alone. Apparent non-unitary behavior of the measurement process is
explained by the arisal of small many particle correlations, that characterize
relaxation.Comment: 13 pages, discussion of pre-measurement added. World Scientific
style. To appear in proceedings "Beyond The Quantum", Th.M. Nieuwenhuizen et
al, eds, (World Scientific, 2007
Mean-field theory of quantum brownian motion
We investigate a mean-field approach to a quantum brownian particle
interacting with a quantum thermal bath at temperature , and subjected to a
non-linear potential. An exact, partially classical description of quantum
brownian motion is proposed, which uses negative probabilities in its
intermediate steps. It is shown that properties of the quantum particle can be
mapped to those of two classical brownian particles in a common potential,
where one of them interacts with the quantum bath, whereas another one
interacts with a classical bath at zero temperature. Due to damping the system
allows a unique and non-singular classical limit at . For high
the stationary state becomes explicitly classical. The low-temperature case is
studied through an effective Fokker-Planck equation. Non-trivial purely quantum
correlation effects between the two particles are found.Comment: 13 pages, 0 figures, revte
The quantum measurement process: an exactly solvable model
An exactly solvable model for a quantum measurement is discussed, that
integrates quantum measurements with classical measurements.
The z-component of a spin-1/2 test spin is measured with an apparatus, that
itself consists of magnet of N spin-1/2 particles, coupled to a bath. The
initial state of the magnet is a metastable paramagnet, while the bath starts
in a thermal, gibbsian state. Conditions are such that the act of measurement
drives the magnet in the up or down ferromagnetic state, according to the sign
of s_z of the test spin.
The quantum measurement goes in two steps. On a timescale 1/\sqrt{N} the
collapse takes place due to a unitary evolution of test spin and apparatus
spins; on a larger but still short timescale this collapse is made definite by
the bath. Then the system is in a `classical' state, having a diagonal density
matrix. The registration of that state is basically a classical process, that
can already be understood from classical statistical mechanics.Comment: 4 pages, presented at the conference "Anomalies and Strange Behavior
in Physics: Challenging the conventional", Napels, April, 2003. v2:
Elaboration on the statistical interpretation of Q
Thomson's formulation of the second law: an exact theorem and limits of its validity
Thomson's formulation of the second law - no work can be extracted from a
system coupled to a bath through a cyclic process - is believed to be a
fundamental principle of nature. For the equilibrium situation a simple proof
is presented, valid for macroscopic sources of work. Thomson's formulation gets
limited when the source of work is mesoscopic, i.e. when its number of degrees
of freedom is large but finite. Here work-extraction from a single equilibrium
thermal bath is possible when its temperature is large enough. This result is
illustrated by means of exactly solvable models. Finally we consider the
Clausius principle: heat goes from high to low temperature. A theorem and some
simple consequences for this statement are pointed out.Comment: 6 pages Latex, uses aip-proceedings style files. Proceedings `Quantum
Limits to the Second Law', San Diego, July 200
Small object limit of Casimir effect and the sign of the Casimir force
We show a simple way of deriving the Casimir Polder interaction, present some
general arguments on the finiteness and sign of mutual Casimir interactions and
finally we derive a simple expression for Casimir radiation from small
accelerated objects.Comment: 13 pages, late
Does the quark-gluon plasma contain stable hadronic bubbles?
We calculate the thermodynamic potential of bubbles of hadrons embedded in
quark-gluon plasma, and of droplets of quark-gluon plasma embedded in hadron
phase. This is a generalization of our previous results to the case of non-zero
chemical potentials. As in the zero chemical potential case, we find that a
quark-gluon plasma in thermodynamic equilibrium may contain stable bubbles of
hadrons of radius fm. The calculations are performed within the
MIT Bag model, using an improved multiple reflection expansion. The results are
of relevance for neutron star phenomenology and for ultrarelativistic heavy ion
collisions.Comment: 12 pages including 8 figures. To appear in Phys. Rev.
Quantum thermodynamics: thermodynamics at the nanoscale
A short introduction on quantum thermodynamics is given and three new topics
are discussed: 1) Maximal work extraction from a finite quantum system. The
thermodynamic prediction fails and a new, general result is derived, the
``ergotropy''. 2) In work extraction from two-temperature setups, the presence
of correlations can push the effective efficiency beyond the Carnot bound. 3)
In the presence of level crossing, non-slow changes may be more optimal than
slow ones.Comment: 5 pages. Talk given at Physics of Quantum Electronics (PQE2004),
Snowbird, by Th.M. Nieuwenhuize
Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula
We derive semiclassical contributions of periodic orbits from a boundary
integral equation for three-dimensional billiard systems. We use an iterative
method that keeps track of the composition of the stability matrix and the
Maslov index as an orbit is traversed. Results are given for isolated periodic
orbits and rotationally invariant families of periodic orbits in axially
symmetric billiard systems. A practical method for determining the stability
matrix and the Maslov index is described.Comment: LaTeX, 19 page
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