1,025 research outputs found
Semiclassical limit of the entanglement in closed pure systems
We discuss the semiclassical limit of the entanglement for the class of
closed pure systems. By means of analytical and numerical calculations we
obtain two main results: (i) the short-time entanglement does not depend on
Planck's constant and (ii) the long-time entanglement increases as more
semiclassical regimes are attained. On one hand, this result is in contrast
with the idea that the entanglement should be destroyed when the macroscopic
limit is reached. On the other hand, it emphasizes the role played by
decoherence in the process of emergence of the classical world. We also found
that, for Gaussian initial states, the entanglement dynamics may be described
by an entirely classical entropy in the semiclassical limit.Comment: 8 pages, 2 figures (accepted for publication in Phys. Rev. A
Time Reversal and n-qubit Canonical Decompositions
For n an even number of qubits and v a unitary evolution, a matrix
decomposition v=k1 a k2 of the unitary group is explicitly computable and
allows for study of the dynamics of the concurrence entanglement monotone. The
side factors k1 and k2 of this Concurrence Canonical Decomposition (CCD) are
concurrence symmetries, so the dynamics reduce to consideration of the a
factor. In this work, we provide an explicit numerical algorithm computing v=k1
a k2 for n odd. Further, in the odd case we lift the monotone to a two-argument
function, allowing for a theory of concurrence dynamics in odd qubits. The
generalization may also be studied using the CCD, leading again to maximal
concurrence capacity for most unitaries. The key technique is to consider the
spin-flip as a time reversal symmetry operator in Wigner's axiomatization; the
original CCD derivation may be restated entirely in terms of this time
reversal. En route, we observe a Kramers' nondegeneracy: the existence of a
nondegenerate eigenstate of any time reversal symmetric n-qubit Hamiltonian
demands (i) n even and (ii) maximal concurrence of said eigenstate. We provide
examples of how to apply this work to study the kinematics and dynamics of
entanglement in spin chain Hamiltonians.Comment: 20 pages, 3 figures; v2 (17pp.): major revision, new abstract,
introduction, expanded bibliograph
Pedestrian Solution of the Two-Dimensional Ising Model
The partition function of the two-dimensional Ising model with zero magnetic
field on a square lattice with m x n sites wrapped on a torus is computed
within the transfer matrix formalism in an explicit step-by-step approach
inspired by Kaufman's work. However, working with two commuting representations
of the complex rotation group SO(2n,C) helps us avoid a number of unnecessary
complications. We find all eigenvalues of the transfer matrix and therefore the
partition function in a straightforward way.Comment: 10 pages, 2 figures; eqs. (101) and (102) corrected, files for fig. 2
fixed, minor beautification
Topological Modes in Dual Lattice Models
Lattice gauge theory with gauge group is reconsidered in four
dimensions on a simplicial complex . One finds that the dual theory,
formulated on the dual block complex , contains topological modes
which are in correspondence with the cohomology group ,
in addition to the usual dynamical link variables. This is a general phenomenon
in all models with single plaquette based actions; the action of the dual
theory becomes twisted with a field representing the above cohomology class. A
similar observation is made about the dual version of the three dimensional
Ising model. The importance of distinct topological sectors is confirmed
numerically in the two dimensional Ising model where they are parameterized by
.Comment: 10 pages, DIAS 94-3
Approach to equilibrium in adiabatically evolving potentials
For a potential function (in one dimension) which evolves from a specified
initial form to a different asymptotically, we study the
evolution, in an overdamped dynamics, of an initial probability density to its
final equilibeium.There can be unexpected effects that can arise from the time
dependence. We choose a time variation of the form
. For a , which is
double welled and a which is simple harmonic, we show that, in
particular, if the evolution is adiabatic, the results in a decrease in the
Kramers time characteristics of . Thus the time dependence makes
diffusion over a barrier more efficient. There can also be interesting
resonance effects when and are two harmonic potentials
displaced with respect to each other that arise from the coincidence of the
intrinsic time scale characterising the potential variation and the Kramers
time.Comment: This paper contains 5 page
Nonequilibrium fluctuation induced escape from a metastable state
Based on a simple microscopic model where the bath is in a non-equilibrium
state we study the escape from a metastable state in the over-damped limit.
Making use of Fokker-Planck-Smoluchowski description we derive the time
dependent escape rate in the non-stationary regime in closed analytical form
which brings on to fore a strong non-exponential kinetic of the system mode.Comment: 4 pages, no figures, EPJ class file include
Kramers-Kronig, Bode, and the meaning of zero
The implications of causality, as captured by the Kramers-Kronig relations
between the real and imaginary parts of a linear response function, are
familiar parts of the physics curriculum. In 1937, Bode derived a similar
relation between the magnitude (response gain) and phase. Although the
Kramers-Kronig relations are an equality, Bode's relation is effectively an
inequality. This perhaps-surprising difference is explained using elementary
examples and ultimately traces back to delays in the flow of information within
the system formed by the physical object and measurement apparatus.Comment: 8 pages; American Journal of Physics, to appea
Cornelius Lanczos's derivation of the usual action integral of classical electrodynamics
The usual action integral of classical electrodynamics is derived starting
from Lanczos's electrodynamics -- a pure field theory in which charged
particles are identified with singularities of the homogeneous Maxwell's
equations interpreted as a generalization of the Cauchy-Riemann regularity
conditions from complex to biquaternion functions of four complex variables. It
is shown that contrary to the usual theory based on the inhomogeneous Maxwell's
equations, in which charged particles are identified with the sources, there is
no divergence in the self-interaction so that the mass is finite, and that the
only approximation made in the derivation are the usual conditions required for
the internal consistency of classical electrodynamics. Moreover, it is found
that the radius of the boundary surface enclosing a singularity interpreted as
an electron is on the same order as that of the hypothetical "bag" confining
the quarks in a hadron, so that Lanczos's electrodynamics is engaging the
reconsideration of many fundamental concepts related to the nature of
elementary particles.Comment: 16 pages. Final version to be published in "Foundations of Physics
Mean first passage time for nuclear fission and the emission of light particles
The concept of a mean first passage time is used to study the time lapse over
which a fissioning system may emit light particles. The influence of the
"transient" and "saddle to scission times" on this emission are critically
examined. It is argued that within the limits of Kramers' picture of fission no
enhancement over that given by his rate formula need to be considered.Comment: 4 pages, RevTex, 4 postscript figures; with correction of misprints;
appeared in Phys. Rev. Lett.90.13270
Numerical Renormalization Group at Criticality
We apply a recently developed numerical renormalization group, the
corner-transfer-matrix renormalization group (CTMRG), to 2D classical lattice
models at their critical temperatures. It is shown that the combination of
CTMRG and the finite-size scaling analysis gives two independent critical
exponents.Comment: 5 pages, LaTeX, 5 figures available upon reques
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