2,800 research outputs found
Condensation of Ideal Bose Gas Confined in a Box Within a Canonical Ensemble
We set up recursion relations for the partition function and the ground-state
occupancy for a fixed number of non-interacting bosons confined in a square box
potential and determine the temperature dependence of the specific heat and the
particle number in the ground state. A proper semiclassical treatment is set up
which yields the correct small-T-behavior in contrast to an earlier theory in
Feynman's textbook on Statistical Mechanics, in which the special role of the
ground state was ignored. The results are compared with an exact quantum
mechanical treatment. Furthermore, we derive the finite-size effect of the
system.Comment: 18 pages, 8 figure
Symmetry Breaking and Order in the Age of Quasicrystals
The discovery of quasicrystals has changed our view of some of the most basic
notions related to the condensed state of matter. Before the age of
quasicrystals, it was believed that crystals break the continuous translation
and rotation symmetries of the liquid-phase into a discrete lattice of
translations, and a finite group of rotations. Quasicrystals, on the other
hand, possess no such symmetries-there are no translations, nor, in general,
are there any rotations, leaving them invariant. Does this imply that no
symmetry is left, or that the meaning of symmetry should be revised? We review
this and other questions related to the liquid-to-crystal symmetry-breaking
transition using the notion of indistinguishability. We characterize the
order-parameter space, describe the different elementary excitations, phonons
and phasons, and discuss the nature of dislocations-keeping in mind that we are
now living in the age of quasicrystals.Comment: To appear in a special issue on quasicrystals of The Israel Journal
of Chemistry, in celebration of the 2011 Nobel Prize in Chemistr
Photon-bunching measurement after 2x25km of standard optical fibers
To show the feasibility of a long distance partial Bell-State measurement, a
Hong-Ou-Mandel experiment with coherent photons is reported. Pairs of
degenerate photons at telecom wavelength are created by parametric down
conversion in a periodically poled lithium niobate waveguide. The photon pairs
are separated in a beam-splitter and transmitted via two fibers of 25km. The
wave-packets are relatively delayed and recombined on a second beam-splitter,
forming a large Mach-Zehnder interferometer. Coincidence counts between the
photons at the two output modes are registered. The main challenge consists in
the trade-off between low count rates due to narrow filtering and length
fluctuations of the 25km long arms during the measurement. For balanced paths a
Hong-Ou-Mandel dip with a visibility of 47.3% is observed, which is close to
the maximal theoretical value of 50% developed here. This proves the
practicability of a long distance Bell state measurement with two independent
sources, as e.g. required in an entanglement swapping configuration in the
scale of tens of km.Comment: 6 pages, 5 figure
Parafermionic phases with symmetry-breaking and topological order
Parafermions are the simplest generalizations of Majorana fermions that
realize topological order. We propose a less restrictive notion of topological
order in 1D open chains, which generalizes the seminal work by Fendley [J.
Stat. Mech., P11020 (2012)]. The first essential property is that the
groundstates are mutually indistinguishable by local, symmetric probes, and the
second is a generalized notion of zero edge modes which cyclically permute the
groundstates. These two properties are shown to be topologically robust, and
applicable to a wider family of topologically-ordered Hamiltonians than has
been previously considered. An an application of these edge modes, we formulate
a new notion of twisted boundary conditions on a closed chain, which guarantees
that the closed-chain groundstate is topological, i.e., it originates from the
topological manifold of degenerate states on the open chain. Finally, we
generalize these ideas to describe symmetry-breaking phases with a
parafermionic order parameter. These exotic phases are condensates of
parafermion multiplets, which generalizes Cooper pairing in superconductors.
The stability of these condensates are investigated on both open and closed
chains.Comment: 27 pages, 9 figure
Lengths May Break Privacy â Or How to Check for Equivalences with Length
Security protocols have been successfully analyzed using symbolic models, where messages are represented by terms and protocols by processes. Privacy properties like anonymity or untraceability are typically expressed as equivalence between processes. While some decision procedures have been proposed for automatically deciding process equivalence, all existing approaches abstract away the information an attacker may get when observing the length of messages.
In this paper, we study process equivalence with length tests. We first show that, in the static case, almost all existing decidability results (for static equivalence) can be extended to cope with length tests.
In the active case, we prove decidability of trace equivalence with length tests, for a bounded number of sessions and for standard primitives. Our result relies on a previous decidability result from Cheval et al (without length tests). Our procedure has been implemented and we have discovered a new flaw against privacy in the biometric passport protocol
Statistics, holography, and black hole entropy in loop quantum gravity
In loop quantum gravity the quantum states of a black hole horizon are
produced by point-like discrete quantum geometry excitations (or {\em
punctures}) labelled by spin . The excitations possibly carry other internal
degrees of freedom also, and the associated quantum states are eigenstates of
the area operator. On the other hand, the appropriately scaled area
operator is also the physical Hamiltonian associated with the
quasilocal stationary observers located at a small distance from the
horizon. Thus, the local energy is entirely accounted for by the geometric
operator .
We assume that: In a suitable vacuum state with regular energy momentum
tensor at and close to the horizon the local temperature measured by stationary
observers is the Unruh temperature and the degeneracy of `matter' states is
exponential with the area ---this is supported by
the well established results of QFT in curved spacetimes, which do not
determine but asserts an exponential behaviour. The geometric
excitations of the horizon (punctures) are indistinguishable. In the
semiclassical limit the area of the black hole horizon is large in Planck
units.
It follows that: Up to quantum corrections, matter degrees of freedom
saturate the holographic bound, {\em viz.} . Up to quantum
corrections, the statistical black hole entropy coincides with
Bekenstein-Hawking entropy . The number of horizon
punctures goes like , i.e the number of punctures
remains large in the semiclassical limit. Fluctuations of the horizon area
are small while fluctuations of the area of an individual puncture are large. A
precise notion of local conformal invariance of the thermal state is recovered
in the limit where the near horizon geometry becomes Rindler
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