5,099 research outputs found
Doubly Special Relativity with a minimum speed and the Uncertainty Principle
The present work aims to search for an implementation of a new symmetry in
the space-time by introducing the idea of an invariant minimum speed scale
(). Such a lowest limit , being unattainable by the particles, represents
a fundamental and preferred reference frame connected to a universal background
field (a vacuum energy) that breaks Lorentz symmetry. So there emerges a new
principle of symmetry in the space-time at the subatomic level for very low
energies close to the background frame (), providing a fundamental
understanding for the uncertainty principle, i.e., the uncertainty relations
should emerge from the space-time with an invariant minimum speed.Comment: 10 pages, 8 figures, Correlated paper in:
http://www.worldscientific.com/worldscinet/ijmpd?journalTabs=read. arXiv
admin note: substantial text overlap with arXiv:physics/0702095,
arXiv:0705.4315, arXiv:0709.1727, arXiv:0805.120
Vacuum energy and Universe in special relativity
The problem of cosmological constant and vacuum energy is usually thought of
as the subject of general relativity. However, the vacuum energy is important
for the Universe even in the absence of gravity, i.e. in the case when the
Newton constant G is exactly zero, G=0. We discuss the response of the vacuum
energy to the perturbations of the quantum vacuum in special relativity, and
find that as in general relativity the vacuum energy density is on the order of
the energy density of matter. In general relativity, the dependence of the
vacuum energy on the equation of state of matter does not contain G, and thus
is valid in the limit when G tends to zero. However, the result obtained for
the vacuum energy in the world without gravity, i.e. when G=0 exactly, is
different.Comment: LaTeX file, 7 pages, no figures, to appear in JETP Letters, reference
is adde
Mesoscopic supersolid of dipoles in a trap
A mesoscopic system of indirect dipolar bosons trapped by a harmonic
potential is considered. The system has a number of physical realizations
including dipole excitons, atoms with large dipolar moment, polar molecules,
Rydberg atoms in inhomogenious electric field. We carry out a diffusion Monte
Carlo simulation to define the quantum properties of a two-dimensional system
of trapped dipoles at zero temperature. In dimensionless units the system is
described by two control parameters, namely the number of particles and the
strength of the interparticle interaction. We have shown that when the
interparticle interaction is strong enough a mesoscopic crystal is formed. As
the strength of interactions is decreased a multi-stage melting takes place.
Off-diagonal order in the system is tested using natural orbitals analysis. We
have found that the system might be Bose-condensed even in the case of strong
interparticle interactions. There is a set of parameters for which a spatially
ordered structure is formed while simultaneously the fraction of Bose condensed
particles is non zero. This might be considered as a realization of a
mesoscopic supersolid.Comment: 5 figure
On the Trace-Free Einstein Equations as a Viable Alternative to General Relativity
The quantum field theoretic prediction for the vacuum energy density leads to
a value for the effective cosmological constant that is incorrect by between 60
to 120 orders of magnitude. We review an old proposal of replacing Einstein's
Field Equations by their trace-free part (the Trace-Free Einstein Equations),
together with an independent assumption of energy--momentum conservation by
matter fields. While this does not solve the fundamental issue of why the
cosmological constant has the value that is observed cosmologically, it is
indeed a viable theory that resolves the problem of the discrepancy between the
vacuum energy density and the observed value of the cosmological constant.
However, one has to check that, as well as preserving the standard cosmological
equations, this does not destroy other predictions, such as the junction
conditions that underlie the use of standard stellar models. We confirm that no
problems arise here: hence, the Trace-Free Einstein Equations are indeed viable
for cosmological and astrophysical applications.Comment: Substantial changes from v1 including added author, change of title
and emphasis of the paper although all original results of v1. remai
OUTLINE OF A GENERALLY COVARIANT QUANTUM FIELD THEORY AND A QUANTUM THEORY OF GRAVITY
We study a tentative generally covariant quantum field theory, denoted the
T-Theory, as a tool to investigate the consistency of quantum general
relativity. The theory describes the gravitational field and a minimally
coupled scalar field; it is based on the loop representation, and on a certain
number of quantization choices. Four-dimensional diffeomorphism-invariant
quantum transition probabilities can be computed from the theory. We present
the explicit calculation of the transition probability between two volume
eigenstates as an example. We discuss the choices on which the T-theory relies,
and the possibilities of modifying them.Comment: Latex file, 33 page
Vortices in fermion droplets with repulsive dipole-dipole interactions
Vortices are found in a fermion system with repulsive dipole-dipole
interactions, trapped by a rotating quasi-two-dimensional harmonic oscillator
potential. Such systems have much in common with electrons in quantum dots,
where rotation is induced via an external magnetic field. In contrast to the
Coulomb interactions between electrons, the (externally tunable) anisotropy of
the dipole-dipole interaction breaks the rotational symmetry of the
Hamiltonian. This may cause the otherwise rotationally symmetric exact
wavefunction to reveal its internal structure more directly.Comment: 5 pages, 5 figure
The Bell states in noncommutative algebraic geometry
We introduce new mathematical aspects of the Bell states using matrix
factorizations, nonnoetherian singularities, and noncommutative blowups. A
matrix factorization of a polynomial consists of two matrices
such that .
Using this notion, we show how the Bell states emerge from the separable
product of two mixtures, by defining pure states over complex matrices rather
than just the complex numbers.
We then show in an idealized algebraic setting that pure states are supported
on nonnoetherian singularities. Moreover, we find that the collapse of a Bell
state is intimately related to the representation theory of the noncommutative
blowup along its singular support. This presents an exchange in geometry: the
nonlocal commutative spacetime of the entangled state emerges from an
underlying local noncommutative spacetime.Comment: 18 pages. Previously titled "Quantum entanglement, emergence, and
noncommutative blowups
On the interaction of a single-photon wave packet with an excited atom
The interaction of a single-photon wave packet with an initially excited
two-level atom in free space is studied in semiclassical and quantum
approaches. It is shown that the final state of the field does not contain
doubly occupied modes. The process of the atom's transition to the ground state
may be accelerated, decelerated or even reversed by the incoming photon,
depending on parameters. The spectrum of emitted radiation is close to the sum
of the spectrum of the incoming single-photon wave packet and the natural line
shape, with small and complicated deviations.Comment: 17 pages, 5 figure
Feshbach-Einstein condensates
We investigate the phase diagram of a two-species Bose-Hubbard model
describing atoms and molecules on a lattice, interacting via a Feshbach
resonance. We identify a region where the system exhibits an exotic super-Mott
phase and regions with phases characterized by atomic and/or molecular
condensates. Our approach is based on a recently developed exact quantum Monte
Carlo algorithm: the Stochastic Green Function algorithm with tunable
directionality. We confirm some of the results predicted by mean-field studies,
but we also find disagreement with these studies. In particular, we find a
phase with an atomic but no molecular condensate, which is missing in all
mean-field phase diagrams.Comment: 4 pages, 6 figure
The Effects of Next-Nearest-Neighbor Interactions on the Orientation Dependence of Step Stiffness: Reconciling Theory with Experiment for Cu(001)
Within the solid-on-solid (SOS) approximation, we carry out a calculation of
the orientational dependence of the step stiffness on a square lattice with
nearest and next-nearest neighbor interactions. At low temperature our result
reduces to a simple, transparent expression. The effect of the strongest trio
(three-site, non pairwise) interaction can easily be incorporated by modifying
the interpretation of the two pairwise energies. The work is motivated by a
calculation based on nearest neighbors that underestimates the stiffness by a
factor of 4 in directions away from close-packed directions, and a subsequent
estimate of the stiffness in the two high-symmetry directions alone that
suggested that inclusion of next-nearest-neighbor attractions could fully
explain the discrepancy. As in these earlier papers, the discussion focuses on
Cu(001).Comment: 8 pages, 3 figures, submitted to Phys. Rev.
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