2,405 research outputs found
A proof of the Kramers degeneracy of transmission eigenvalues from antisymmetry of the scattering matrix
In time reversal symmetric systems with half integral spins (or more
concretely, systems with an antiunitary symmetry that squares to -1 and
commutes with the Hamiltonian) the transmission eigenvalues of the scattering
matrix come in pairs. We present a proof of this fact that is valid both for
even and odd number of modes and relies solely on the antisymmetry of the
scattering matrix imposed by time reversal symmetry.Comment: 2 page
Critique of proposed limit to space--time measurement, based on Wigner's clocks and mirrors
Based on a relation between inertial time intervals and the Riemannian
curvature, we show that space--time uncertainty derived by Ng and van Dam
implies absurd uncertainties of the Riemannian curvature.Comment: 5 pages, LaTex, field "Author:" correcte
Excitations and Quantum Fluctuations in Site Diluted Two-Dimensional Antiferromagnets
We study the effect of site dilution and quantum fluctuations in an
antiferromagnetic spin system on a square lattice within the linear spin-wave
approximation. By performing numerical diagonalization in real space and
finite-size scaling, we characterize the nature of the low-energy spin
excitations for different dilution fractions up to the classical percolation
threshold. We find nontrivial signatures of fractonlike excitations at high
frequencies. Our simulations also confirm the existence of an upper bound for
the amount of quantum fluctuations in the ground state of the system, leading
to the persistence of long-range order up to the percolation threshold. This
result is in agreement with recent neutron-scattering experimental data and
quantum Monte Carlo numerical calculations. We also show that the absence of a
quantum critical point below the classical percolation threshold holds for a
large class of systems whose Hamiltonians can be mapped onto a system of
coupled noninteracting massless bosons.Comment: RevTex 4, 16 pages, 8 EPS figures, typos corrected, data from Ref. 9
added, few minor changes in the text, to appear in Phys. Rev.
Quantum reference frames and deformed symmetries
In the context of constrained quantum mechanics, reference systems are used
to construct relational observables that are invariant under the action of the
symmetry group. Upon measurement of a relational observable, the reference
system undergoes an unavoidable measurement "back-action" that modifies its
properties. In a quantum-gravitational setting, it has been argued that such a
back-action may produce effects that are described at an effective level as a
form of deformed (or doubly) special relativity. We examine this possibility
using a simple constrained system that has been extensively studied in the
context of quantum information. While our conclusions support the idea of a
symmetry deformation, they also reveal a host of other effects that may be
relevant to the context of quantum gravity, and could potentially conceal the
symmetry deformation.Comment: 11 pages, revtex. Comments are welcom
An exactly solvable self-convolutive recurrence
We consider a self-convolutive recurrence whose solution is the sequence of
coefficients in the asymptotic expansion of the logarithmic derivative of the
confluent hypergeometic function . By application of the Hilbert
transform we convert this expression into an explicit, non-recursive solution
in which the th coefficient is expressed as the th moment of a
measure, and also as the trace of the th iterate of a linear operator.
Applications of these sequences, and hence of the explicit solution provided,
are found in quantum field theory as the number of Feynman diagrams of a
certain type and order, in Brownian motion theory, and in combinatorics
Quantum chaos: an introduction via chains of interacting spins-1/2
We introduce aspects of quantum chaos by analyzing the eigenvalues and the
eigenstates of quantum many-body systems. The properties of quantum systems
whose classical counterparts are chaotic differ from those whose classical
counterparts are not chaotic. The spectrum of the first exhibits repulsion of
the energy levels. This is one of the main signatures of quantum chaos. We show
how level repulsion develops in one-dimensional systems of interacting spins
1/2 which are devoid of random elements and involve only two-body interactions.
In addition to the statistics of the eigenvalues, we analyze how the structure
of the eigenstates may indicate chaos. The programs used to obtain the data are
available online.Comment: 7 pages, 3 figure
Quantum coherence in the presence of unobservable quantities
State representations summarize our knowledge about a system. When
unobservable quantities are introduced the state representation is typically no
longer unique. However, this non-uniqueness does not affect subsequent
inferences based on any observable data. We demonstrate that the inference-free
subspace may be extracted whenever the quantity's unobservability is guaranteed
by a global conservation law. This result can generalize even without such a
guarantee. In particular, we examine the coherent-state representation of a
laser where the absolute phase of the electromagnetic field is believed to be
unobservable. We show that experimental coherent states may be separated from
the inference-free subspaces induced by this unobservable phase. These physical
states may then be approximated by coherent states in a relative-phase Hilbert
space
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