88 research outputs found
The two-dimensional hydrogen atom revisited
The bound state energy eigenvalues for the two-dimensional Kepler problem are
found to be degenerate. This "accidental" degeneracy is due to the existence of
a two-dimensional analogue of the quantum-mechanical Runge-Lenz vector.
Reformulating the problem in momentum space leads to an integral form of the
Schroedinger equation. This equation is solved by projecting the
two-dimensional momentum space onto the surface of a three-dimensional sphere.
The eigenfunctions are then expanded in terms of spherical harmonics, and this
leads to an integral relation in terms of special functions which has not
previously been tabulated. The dynamical symmetry of the problem is also
considered, and it is shown that the two components of the Runge-Lenz vector in
real space correspond to the generators of infinitesimal rotations about the
respective coordinate axes in momentum space.Comment: 10 pages, no figures, RevTex
Heat transfer and Fourier's law in off-equilibrium systems
We study the most suitable procedure to measure the effective temperature in
off-equilibrium systems. We analyze the stationary current established between
an off-equilibrium system and a thermometer and the necessary conditions for
that current to vanish. We find that the thermometer must have a short
characteristic time-scale compared to the typical decorrelation time of the
glassy system to correctly measure the effective temperature. This general
conclusion is confirmed analyzing an ensemble of harmonic oscillators with
Monte Carlo dynamics as an illustrative example of a solvable model of a glass.
We also find that the current defined allows to extend Fourier's law to the
off-equilibrium regime by consistently defining effective transport
coefficients. Our results for the oscillator model explain why thermal
conductivities between thermalized and frozen degrees of freedom in structural
glasses are extremely small.Comment: 7 pages, REVTeX, 4 eps figure
Unitary transformations for testing Bell inequalities
It is shown that optical experimental tests of Bell inequality violations can
be described by SU(1,1) transformations of the vacuum state, followed by photon
coincidence detections. The set of all possible tests are described by various
SU(1,1) subgroups of Sp(8,). In addition to establishing a common
formalism for physically distinct Bell inequality tests, the similarities and
differences of post--selected tests of Bell inequality violations are also made
clear. A consequence of this analysis is that Bell inequality tests are
performed on a very general version of SU(1,1) coherent states, and the
theoretical violation of the Bell inequality by coincidence detection is
calculated and discussed. This group theoretical approach to Bell states is
relevant to Bell state measurements, which are performed, for example, in
quantum teleportation.Comment: 3 figure
Universal amplitude ratios of two-dimensional percolation from field theory
We complete the determination of the universal amplitude ratios of
two-dimensional percolation within the two-kink approximation of the form
factor approach. For the cluster size ratio, which has for a long time been
elusive both theoretically and numerically, we obtain the value 160.2, in good
agreement with the lattice estimate 162.5 +/- 2 of Jensen and Ziff.Comment: 8 page
Exact, E=0, Solutions for General Power-Law Potentials. I. Classical Orbits
For zero energy, , we derive exact, classical solutions for {\em all}
power-law potentials, , with and . When the angular momentum is non-zero, these solutions lead to
the orbits , for all . When , the orbits are bound and go through the origin.
This leads to discrete discontinuities in the functional dependence of
and , as functions of , as the orbits pass through the origin. We
describe a procedure to connect different analytic solutions for successive
orbits at the origin. We calculate the periods and precessions of these bound
orbits, and graph a number of specific examples. Also, we explain why they all
must violate the virial theorem. The unbound orbits are also discussed in
detail. This includes the unusual orbits which have finite travel times to
infinity and also the special case.Comment: LaTeX, 27 pages with 12 figures available from the authors or can be
generated from Mathematica instructions at end of the fil
Excess number of percolation clusters on the surface of a sphere
Monte Carlo simulations were performed in order to determine the excess
number of clusters b and the average density of clusters n_c for the
two-dimensional "Swiss cheese" continuum percolation model on a planar L x L
system and on the surface of a sphere. The excess number of clusters for the L
x L system was confirmed to be a universal quantity with a value b = 0.8841 as
previously predicted and verified only for lattice percolation. The excess
number of clusters on the surface of a sphere was found to have the value b =
1.215(1) for discs with the same coverage as the flat critical system. Finally,
the average critical density of clusters was calculated for continuum systems
n_c = 0.0408(1).Comment: 13 pages, 2 figure
Test of Universality in the Ising Spin Glass Using High Temperature Graph Expansion
We calculate high-temperature graph expansions for the Ising spin glass model
with 4 symmetric random distribution functions for its nearest neighbor
interaction constants J_{ij}. Series for the Edwards-Anderson susceptibility
\chi_EA are obtained to order 13 in the expansion variable (J/(k_B T))^2 for
the general d-dimensional hyper-cubic lattice, where the parameter J determines
the width of the distributions. We explain in detail how the expansions are
calculated. The analysis, using the Dlog-Pad\'e approximation and the
techniques known as M1 and M2, leads to estimates for the critical threshold
(J/(k_B T_c))^2 and for the critical exponent \gamma in dimensions 4, 5, 7 and
8 for all the distribution functions. In each dimension the values for \gamma
agree, within their uncertainty margins, with a common value for the different
distributions, thus confirming universality.Comment: 13 figure
Entangling power and operator entanglement in qudit systems
We establish the entangling power of a unitary operator on a general
finite-dimensional bipartite quantum system with and without ancillas, and give
relations between the entangling power based on the von Neumann entropy and the
entangling power based on the linear entropy. Significantly, we demonstrate
that the entangling power of a general controlled unitary operator acting on
two equal-dimensional qudits is proportional to the corresponding operator
entanglement if linear entropy is adopted as the quantity representing the
degree of entanglement. We discuss the entangling power and operator
entanglement of three representative quantum gates on qudits: the SUM, double
SUM, and SWAP gates.Comment: 8 pages, 1 figure. Version 3: Figure was improved and the MS was a
bit shortene
Quantum gates on hybrid qudits
We introduce quantum hybrid gates that act on qudits of different dimensions.
In particular, we develop two representative two-qudit hybrid gates (SUM and
SWAP) and many-qudit hybrid Toffoli and Fredkin gates. We apply the hybrid SUM
gate to generating entanglement, and find that operator entanglement of the SUM
gate is equal to the entanglement generated by it for certain initial states.
We also show that the hybrid SUM gate acts as an automorphism on the Pauli
group for two qudits of different dimension under certain conditions. Finally,
we describe a physical realization of these hybrid gates for spin systems.Comment: 8 pages and 1 figur
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