423 research outputs found
Measuring Energy, Estimating Hamiltonians, and the Time-Energy Uncertainty Relation
Suppose that the Hamiltonian acting on a quantum system is unknown and one
wants to determine what is the Hamiltonian. We show that in general this
requires a time which obeys the uncertainty relation where is a measure of how accurately the unknown
Hamiltonian must be estimated. We then apply this result to the problem of
measuring the energy of an unknown quantum state. It has been previously shown
that if the Hamiltonian is known, then the energy can in principle be measured
in an arbitrarily short time. On the other hand we show that if the Hamiltonian
is not known then an energy measurement necessarily takes a minimum time
which obeys the uncertainty relation
where is the precision of the energy measurement. Several examples
are studied to address the question of whether it is possible to saturate these
uncertainty relations. Their interpretation is discussed in detail.Comment: 12pages, revised version with small correction
Hamiltonian Formalism of the de-Sitter Invariant Special Relativity
Lagrangian of the Einstein's special relativity with universal parameter
() is invariant under Poincar\'e transformation which preserves
Lorentz metric . The has been extended to be
one which is invariant under de Sitter transformation that preserves so called
Beltrami metric . There are two universal parameters and in
this Special Relativity (denote it as ). The
Lagrangian-Hamiltonian formulism of is formulated in this
paper. The canonic energy, canonic momenta, and 10 Noether charges
corresponding to the space-time's de Sitter symmetry are derived. The canonical
quantization of the mechanics for -free particle is
performed. The physics related to it is discussed.Comment: 24 pages, no figur
Strong Phase Separation in a Model of Sedimenting Lattices
We study the steady state resulting from instabilities in crystals driven
through a dissipative medium, for instance, a colloidal crystal which is
steadily sedimenting through a viscous fluid. The problem involves two coupled
fields, the density and the tilt; the latter describes the orientation of the
mass tensor with respect to the driving field. We map the problem to a 1-d
lattice model with two coupled species of spins evolving through conserved
dynamics. In the steady state of this model each of the two species shows
macroscopic phase separation. This phase separation is robust and survives at
all temperatures or noise levels--- hence the term Strong Phase Separation.
This sort of phase separation can be understood in terms of barriers to
remixing which grow with system size and result in a logarithmically slow
approach to the steady state. In a particular symmetric limit, it is shown that
the condition of detailed balance holds with a Hamiltonian which has
infinite-ranged interactions, even though the initial model has only local
dynamics. The long-ranged character of the interactions is responsible for
phase separation, and for the fact that it persists at all temperatures.
Possible experimental tests of the phenomenon are discussed.Comment: To appear in Phys Rev E (1 January 2000), 16 pages, RevTex, uses
epsf, three ps figure
Nonmonotonic dependence of the absolute entropy on temperature in supercooled Stillinger-Weber silicon
Using a recently developed thermodynamic integration method, we compute the
precise values of the excess Gibbs free energy (G^e) of the high density liquid
(HDL) phase with respect to the crystalline phase at different temperatures (T)
in the supercooled region of the Stillinger-Weber (SW) silicon [F. H.
Stillinger and T. A. Weber, Phys. Rev. B. 32, 5262 (1985)]. Based on the slope
of G^e with respect to T, we find that the absolute entropy of the HDL phase
increases as its enthalpy changes from the equilibrium value at T \ge 1065 K to
the value corresponding to a non-equilibrium state at 1060 K. We find that the
volume distribution in the equilibrium HDL phases become progressively broader
as the temperature is reduced to 1060 K, exhibiting van-der-Waals (VDW) loop in
the pressure-volume curves. Our results provides insight into the thermodynamic
cause of the transition from the HDL phase to the low density phases in SW
silicon, observed in earlier studies near 1060 K at zero pressure.Comment: This version is accepted for publication in Journal of Statistical
Physics (11 figures, 1 table
Microfluidic and Nanofluidic Cavities for Quantum Fluids Experiments
The union of quantum fluids research with nanoscience is rich with
opportunities for new physics. The relevant length scales in quantum fluids,
3He in particular, are comparable to those possible using microfluidic and
nanofluidic devices. In this article, we will briefly review how the physics of
quantum fluids depends strongly on confinement on the microscale and nanoscale.
Then we present devices fabricated specifically for quantum fluids research,
with cavity sizes ranging from 30 nm to 11 microns deep, and the
characterization of these devices for low temperature quantum fluids
experiments.Comment: 12 pages, 3 figures, Accepted to Journal of Low Temperature Physic
A Model for the Stray Light Contamination of the UVCS Instrument on SOHO
We present a detailed model of stray-light suppression in the spectrometer
channels of the Ultraviolet Coronagraph Spectrometer (UVCS) on the SOHO
spacecraft. The control of diffracted and scattered stray light from the bright
solar disk is one of the most important tasks of a coronagraph. We compute the
fractions of light that diffract past the UVCS external occulter and
non-specularly pass into the spectrometer slit. The diffracted component of the
stray light depends on the finite aperture of the primary mirror and on its
figure. The amount of non-specular scattering depends mainly on the
micro-roughness of the mirror. For reasonable choices of these quantities, the
modeled stray-light fraction agrees well with measurements of stray light made
both in the laboratory and during the UVCS mission. The models were constructed
for the bright H I Lyman alpha emission line, but they are applicable to other
spectral lines as well.Comment: 19 pages, 5 figures, Solar Physics, in pres
On the gravitational, dilatonic and axionic radiative damping of cosmic strings
We study the radiation reaction on cosmic strings due to the emission of
dilatonic, gravitational and axionic waves. After verifying the (on average)
conservative nature of the time-symmetric self-interactions, we concentrate on
the finite radiation damping force associated with the half-retarded minus
half-advanced ``reactive'' fields. We revisit a recent proposal of using a
``local back reaction approximation'' for the reactive fields. Using
dimensional continuation as convenient technical tool, we find, contrary to
previous claims, that this proposal leads to antidamping in the case of the
axionic field, and to zero (integrated) damping in the case of the
gravitational field. One gets normal positive damping only in the case of the
dilatonic field. We propose to use a suitably modified version of the local
dilatonic radiation reaction as a substitute for the exact (non-local)
gravitational radiation reaction. The incorporation of such a local
approximation to gravitational radiation reaction should allow one to complete,
in a computationally non-intensive way, string network simulations and to give
better estimates of the amount and spectrum of gravitational radiation emitted
by a cosmologically evolving network of massive strings.Comment: 48 pages, RevTex, epsfig, 1 figure; clarification of the domain of
validity of the perturbative derivation of the string equations of motion,
and of their renormalizabilit
Some anisotropic universes in the presence of imperfect fluid coupling with spatial curvature
We consider Bianchi VI spacetime, which also can be reduced to Bianchi types
VI0-V-III-I. We initially consider the most general form of the energy-momentum
tensor which yields anisotropic stress and heat flow. We then derive an
energy-momentum tensor that couples with the spatial curvature in a way so as
to cancel out the terms that arise due to the spatial curvature in the
evolution equations of the Einstein field equations. We obtain exact solutions
for the universes indefinetly expanding with constant mean deceleration
parameter. The solutions are beriefly discussed for each Bianchi type. The
dynamics of the models and fluid are examined briefly, and the models that can
approach to isotropy are determined. We conclude that even if the observed
universe is almost isotropic, this does not necessarily imply the isotropy of
the fluid (e.g., dark energy) affecting the evolution of the universe within
the context of general relativity.Comment: 17 pages, no figures; to appear in International Journal of
Theoretical Physics; in this version (which is more concise) an equation
added, some references updated and adde
Higher Grading Conformal Affine Toda Teory and (Generalized) Sine-Gordon/Massive Thirring Duality
Some properties of the higher grading integrable generalizations of the
conformal affine Toda systems are studied. The fields associated to the
non-zero grade generators are Dirac spinors. The effective action is written in
terms of the Wess-Zumino-Novikov-Witten (WZNW) action associated to an affine
Lie algebra, and an off-critical theory is obtained as the result of the
spontaneous breakdown of the conformal symmetry. Moreover, the off-critical
theory presents a remarkable equivalence between the Noether and topological
currents of the model. Related to the off-critical model we define a real and
local Lagrangian provided some reality conditions are imposed on the fields of
the model. This real action model is expected to describe the soliton sector of
the original model, and turns out to be the master action from which we uncover
the weak-strong phases described by (generalized) massive Thirring and
sine-Gordon type models, respectively. The case of any (untwisted) affine Lie
algebra furnished with the principal gradation is studied in some detail.
The example of is presented explicitly.Comment: 28 pages, JHEP styl
The Possibilist Transactional Interpretation and Relativity
A recent ontological variant of Cramer's Transactional Interpretation, called
"Possibilist Transactional Interpretation" or PTI, is extended to the
relativistic domain. The present interpretation clarifies the concept of
'absorption,' which plays a crucial role in TI (and in PTI). In particular, in
the relativistic domain, coupling amplitudes between fields are interpreted as
amplitudes for the generation of confirmation waves (CW) by a potential
absorber in response to offer waves (OW), whereas in the nonrelativistic
context CW are taken as generated with certainty. It is pointed out that
solving the measurement problem requires venturing into the relativistic domain
in which emissions and absorptions take place; nonrelativistic quantum
mechanics only applies to quanta considered as 'already in existence' (i.e.,
'free quanta'), and therefore cannot fully account for the phenomenon of
measurement, in which quanta are tied to sources and sinks.Comment: Final version with some minor corrections as published in Foundations
of Physics. This paper has significant overlap with Chapter 6 of my book on
the Transactional Interpretation, forthcoming from Cambridge University
Press:
http://www.cambridge.org/us/knowledge/isbn/item6860644/?site_locale=en_US
(Additional preview material is available at rekastner.wordpress.com)
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