140 research outputs found
Dispersion interaction between crossed conducting wires
We compute the Van der Waals (nonretarded Casimir) interaction energy
between two infinitely long, crossed conducting wires separated by a
minimum distance much greater than their radius. We find that, up to a
logarithmic correction factor,
where is a smooth bounded function of the angle between
the wires. We recover a conventional result of the form when we include an electronic energy gap
in our calculation. Our prediction of gap-dependent energetics may be
observable experimentally for carbon nanotubes, either via AFM detection of the
vdW force or torque, or indirectly via observation of mechanical oscillations.
This shows that strictly parallel wires, as assumed in previous predictions,
are not needed to see a novel effect of this type.Comment: 4 pp, 1 fig, 1 tabl
Parity violating cylindrical shell in the framework of QED
We present calculations of Casimir energy (CE) in a system of quantized
electromagnetic (EM) field interacting with an infinite circular cylindrical
shell (which we call `the defect'). Interaction is described in the only
QFT-consistent way by Chern-Simon action concentrated on the defect, with a
single coupling constant .
For regularization of UV divergencies of the theory we use % physically
motivated Pauli-Villars regularization of the free EM action. The divergencies
are extracted as a polynomial in regularization mass , and they renormalize
classical part of the surface action.
We reveal the dependence of CE on the coupling constant . Corresponding
Casimir force is attractive for all values of . For we
reproduce the known results for CE for perfectly conducting cylindrical shell
first obtained by DeRaad and Milton.Comment: Typos corrected. Some references adde
The Casimir effect as scattering problem
We show that Casimir-force calculations for a finite number of
non-overlapping obstacles can be mapped onto quantum-mechanical billiard-type
problems which are characterized by the scattering of a fictitious point
particle off the very same obstacles. With the help of a modified Krein trace
formula the genuine/finite part of the Casimir energy is determined as the
energy-weighted integral over the log-determinant of the multi-scattering
matrix of the analog billiard problem. The formalism is self-regulating and
inherently shows that the Casimir energy is governed by the infrared end of the
multi-scattering phase shifts or spectrum of the fluctuating field. The
calculation is exact and in principle applicable for any separation(s) between
the obstacles. In practice, it is more suited for large- to medium-range
separations. We report especially about the Casimir energy of a fluctuating
massless scalar field between two spheres or a sphere and a plate under
Dirichlet and Neumann boundary conditions. But the formalism can easily be
extended to any number of spheres and/or planes in three or arbitrary
dimensions, with a variety of boundary conditions or non-overlapping
potentials/non-ideal reflectors.Comment: 14 pages, 2 figures, plenary talk at QFEXT07, Leipzig, September
2007, some typos correcte
Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity
From the beginning of the subject, calculations of quantum vacuum energies or
Casimir energies have been plagued with two types of divergences: The total
energy, which may be thought of as some sort of regularization of the
zero-point energy, , seems manifestly divergent. And
local energy densities, obtained from the vacuum expectation value of the
energy-momentum tensor, , typically diverge near
boundaries. The energy of interaction between distinct rigid bodies of whatever
type is finite, corresponding to observable forces and torques between the
bodies, which can be unambiguously calculated. The self-energy of a body is
less well-defined, and suffers divergences which may or may not be removable.
Some examples where a unique total self-stress may be evaluated include the
perfectly conducting spherical shell first considered by Boyer, a perfectly
conducting cylindrical shell, and dilute dielectric balls and cylinders. In
these cases the finite part is unique, yet there are divergent contributions
which may be subsumed in some sort of renormalization of physical parameters.
The divergences that occur in the local energy-momentum tensor near surfaces
are distinct from the divergences in the total energy, which are often
associated with energy located exactly on the surfaces. However, the local
energy-momentum tensor couples to gravity, so what is the significance of
infinite quantities here? For the classic situation of parallel plates there
are indications that the divergences in the local energy density are consistent
with divergences in Einstein's equations; correspondingly, it has been shown
that divergences in the total Casimir energy serve to precisely renormalize the
masses of the plates, in accordance with the equivalence principle.Comment: 53 pages, 1 figure, invited review paper to Lecture Notes in Physics
volume in Casimir physics edited by Diego Dalvit, Peter Milonni, David
Roberts, and Felipe da Ros
Decoherence by engineered quantum baths
We introduce, and determine decoherence for, a wide class of non-trivial
quantum spin baths which embrace Ising, XY and Heisenberg universality classes
coupled to a two-level system. For the XY and Ising universality classes we
provide an exact expression for the decay of the loss of coherence beyond the
case of a central spin coupled uniformly to all the spins of the baths which
has been discussed so far in the literature. In the case of the Heisenberg spin
bath we study the decoherence by means of the time-dependent density matrix
renormalization group. We show how these baths can be engineered, by using
atoms in optical lattices.Comment: 4 pages, 4 figure
Can One Trust Quantum Simulators?
Various fundamental phenomena of strongly-correlated quantum systems such as
high- superconductivity, the fractional quantum-Hall effect, and quark
confinement are still awaiting a universally accepted explanation. The main
obstacle is the computational complexity of solving even the most simplified
theoretical models that are designed to capture the relevant quantum
correlations of the many-body system of interest. In his seminal 1982 paper
[Int. J. Theor. Phys. 21, 467], Richard Feynman suggested that such models
might be solved by "simulation" with a new type of computer whose constituent
parts are effectively governed by a desired quantum many-body dynamics.
Measurements on this engineered machine, now known as a "quantum simulator,"
would reveal some unknown or difficult to compute properties of a model of
interest. We argue that a useful quantum simulator must satisfy four
conditions: relevance, controllability, reliability, and efficiency. We review
the current state of the art of digital and analog quantum simulators. Whereas
so far the majority of the focus, both theoretically and experimentally, has
been on controllability of relevant models, we emphasize here the need for a
careful analysis of reliability and efficiency in the presence of
imperfections. We discuss how disorder and noise can impact these conditions,
and illustrate our concerns with novel numerical simulations of a paradigmatic
example: a disordered quantum spin chain governed by the Ising model in a
transverse magnetic field. We find that disorder can decrease the reliability
of an analog quantum simulator of this model, although large errors in local
observables are introduced only for strong levels of disorder. We conclude that
the answer to the question "Can we trust quantum simulators?" is... to some
extent.Comment: 20 pages. Minor changes with respect to version 2 (some additional
explanations, added references...
Entanglement spectrum degeneracy and the Cardy formula in 1+1 dimensional conformal field theories
We investigate the effect of a global degeneracy in the distribution of the entanglement spectrum in conformal field theories in one spatial dimension. We relate the recently found universal expression for the entanglement Hamiltonian to the distribution of the entanglement spectrum. The main tool to establish this connection is the Cardy formula. It turns out that the Affleck-Ludwig non-integer degeneracy, appearing because of the boundary conditions induced at the entangling surface, can be directly read from the entanglement spectrum distribution. We also clarify the effect of the noninteger degeneracy on the spectrum of the partial transpose, which is the central object for quantifying the entanglement in mixed states. We show that the exact knowledge of the entanglement spectrum in some integrable spinchains provides strong analytical evidences corroborating our results
From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
We derive exact formulas for the expectation value of local observables in a one-dimensional gas of bosons with point-wise repulsive interactions (Lieb-Liniger model). Starting from a recently conjectured expression for the expectation value of vertex operators in the sinh-Gordon field theory, we derive explicit analytic expressions for the one-point K-body correlation functions \u27e8(\u3a8\u2020)K(\u3a8)K\u27e9 in the Lieb-Liniger gas, for arbitrary integer K. These are valid for all excited states in the thermodynamic limit, including thermal states, generalized Gibbs ensembles and non-equilibrium steady states arising in transport settings. Our formulas display several physically interesting applications: most prominently, they allow us to compute the full counting statistics for the particle-number fluctuations in a short interval. Furthermore, combining our findings with the recently introduced generalized hydrodynamics, we are able to study multi-point correlation functions at the Eulerian scale in non-homogeneous settings. Our results complement previous studies in the literature and provide a full solution to the problem of computing one-point functions in the Lieb Liniger model
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