7,085 research outputs found
Nonlocal effects in Fock space
If a physical system contains a single particle, and if two distant detectors
test the presence of linear superpositions of one-particle and vacuum states, a
violation of classical locality can occur. It is due to the creation of a
two-particle component by the detecting process itself.Comment: final version in PRL 74 (1995) 4571; 76 (1996) 2205 (erratum
Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions
We derive the energy levels associated with the even-parity wave functions of
the harmonic oscillator with an additional delta-function potential at the
origin. Our results bring to the attention of students a non-trivial and
analytical example of a modification of the usual harmonic oscillator
potential, with emphasis on the modification of the boundary conditions at the
origin. This problem calls the attention of the students to an inaccurate
statement in quantum mechanics textbooks often found in the context of solution
of the harmonic oscillator problem.Comment: 9 pages, 3 figure
Testing quantum superpositions of the gravitational field with Bose-Einstein condensates
We consider the gravity field of a Bose-Einstein condensate in a quantum
superposition. The gravity field then is also in a quantum superposition which
is in principle observable. Hence we have ``quantum gravity'' far away from the
so-called Planck scale
Bell's inequality with Dirac particles
We study Bell's inequality using the Bell states constructed from four
component Dirac spinors. Spin operator is related to the Pauli-Lubanski pseudo
vector which is relativistic invariant operator. By using Lorentz
transformation, in both Bell states and spin operator, we obtain an observer
independent Bell's inequality, so that it is maximally violated as long as it
is violated maximally in the rest frame.Comment: 7 pages. arXiv admin note: text overlap with arXiv:quant-ph/0308156
by other author
Cutoff for the noisy voter model
Given a continuous time Markov Chain on a finite set , the
associated noisy voter model is the continuous time Markov chain on
, which evolves in the following way: (1) for each two sites and
in , the state at site changes to the value of the state at site
at rate ; (2) each site rerandomizes its state at rate 1. We show that
if there is a uniform bound on the rates and the corresponding
stationary distributions are almost uniform, then the mixing time has a sharp
cutoff at time with a window of order 1. Lubetzky and Sly proved
cutoff with a window of order 1 for the stochastic Ising model on toroids; we
obtain the special case of their result for the cycle as a consequence of our
result. Finally, we consider the model on a star and demonstrate the surprising
phenomenon that the time it takes for the chain started at all ones to become
close in total variation to the chain started at all zeros is of smaller order
than the mixing time.Comment: Published at http://dx.doi.org/10.1214/15-AAP1108 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Dynamical polarizability of graphene beyond the Dirac cone approximation
We compute the dynamical polarizability of graphene beyond the usual Dirac
cone approximation, integrating over the full Brillouin zone. We find
deviations at ( the hopping parameter) which amount to a
logarithmic singularity due to the van Hove singularity and derive an
approximate analytical expression. Also at low energies, we find deviations
from the results obtained from the Dirac cone approximation which manifest
themselves in a peak spitting at arbitrary direction of the incoming wave
vector \q. Consequences for the plasmon spectrum are discussed.Comment: 8 pages, 6 figure
The dimension of the Brownian frontier is greater than 1
Consider a planar Brownian motion run for finite time. The frontier or
``outer boundary'' of the path is the boundary of the unbounded component of
the complement. Burdzy (1989) showed that the frontier has infinite length. We
improve this by showing that the Hausdorff dimension of the frontier is
strictly greater than 1. (It has been conjectured that the Brownian frontier
has dimension , but this is still open.) The proof uses Jones's Traveling
Salesman Theorem and a self-similar tiling of the plane by fractal tiles known
as Gosper Islands
Determinantal Processes and Independence
We give a probabilistic introduction to determinantal and permanental point
processes. Determinantal processes arise in physics (fermions, eigenvalues of
random matrices) and in combinatorics (nonintersecting paths, random spanning
trees). They have the striking property that the number of points in a region
is a sum of independent Bernoulli random variables, with parameters which
are eigenvalues of the relevant operator on . Moreover, any
determinantal process can be represented as a mixture of determinantal
projection processes. We give a simple explanation for these known facts, and
establish analogous representations for permanental processes, with geometric
variables replacing the Bernoulli variables. These representations lead to
simple proofs of existence criteria and central limit theorems, and unify known
results on the distribution of absolute values in certain processes with
radially symmetric distributions.Comment: Published at http://dx.doi.org/10.1214/154957806000000078 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Nonlocality with less Complementarity
In quantum mechanics, nonlocality (a violation of a Bell inequality) is
intimately linked to complementarity, by which we mean that consistently
assigning values to different observables at the same time is not possible.
Nonlocality can only occur when some of the relevant observables do not
commute, and this noncommutativity makes the observables complementary. Beyond
quantum mechanics, the concept of complementarity can be formalized in several
distinct ways. Here we describe some of these possible formalizations and ask
how they relate to nonlocality. We partially answer this question by describing
two toy theories which display nonlocality and obey the no-signaling principle,
although each of them does not display a certain kind of complementarity. The
first toy theory has the property that it maximally violates the CHSH
inequality, although the corresponding local observables are pairwise jointly
measurable. The second toy theory also maximally violates the CHSH inequality,
although its state space is classical and all measurements are mutually
nondisturbing: if a measurement sequence contains some measurement twice with
any number of other measurements in between, then these two measurements give
the same outcome with certainty.Comment: 6 pages, published versio
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