86,753 research outputs found
Non-Markovian Dynamics and Entanglement of Two-level Atoms in a Common Field
We derive the stochastic equations and consider the non-Markovian dynamics of
a system of multiple two-level atoms in a common quantum field. We make only
the dipole approximation for the atoms and assume weak atom-field interactions.
From these assumptions we use a combination of non-secular open- and
closed-system perturbation theory, and we abstain from any additional
approximation schemes. These more accurate solutions are necessary to explore
several regimes: in particular, near-resonance dynamics and low-temperature
behavior. In detuned atomic systems, small variations in the system energy
levels engender timescales which, in general, cannot be safely ignored, as
would be the case in the rotating-wave approximation (RWA). More problematic
are the second-order solutions, which, as has been recently pointed out, cannot
be accurately calculated using any second-order perturbative master equation,
whether RWA, Born-Markov, Redfield, etc.. This latter problem, which applies to
all perturbative open-system master equations, has a profound effect upon
calculation of entanglement at low temperatures. We find that even at zero
temperature all initial states will undergo finite-time disentanglement
(sometimes termed "sudden death"), in contrast to previous work. We also use
our solution, without invoking RWA, to characterize the necessary conditions
for Dickie subradiance at finite temperature. We find that the subradiant
states fall into two categories at finite temperature: one that is temperature
independent and one that acquires temperature dependence. With the RWA there is
no temperature dependence in any case.Comment: 17 pages, 13 figures, v2 updated references, v3 clarified results and
corrected renormalization, v4 further clarified results and new Fig. 8-1
Off-diagonal matrix elements of local operators in many-body quantum systems
In the time evolution of isolated quantum systems out of equilibrium, local
observables generally relax to a long-time asymptotic value, governed by the
expectation values (diagonal matrix elements) of the corresponding operator in
the eigenstates of the system. The temporal fluctuations around this value,
response to further perturbations, and the relaxation toward this asymptotic
value, are all determined by the off-diagonal matrix elements. Motivated by
this non-equilibrium role, we present generic statistical properties of
off-diagonal matrix elements of local observables in two families of
interacting many-body systems with local interactions. Since integrability (or
lack thereof) is an important ingredient in the relaxation process, we analyze
models that can be continuously tuned to integrability. We show that, for
generic non-integrable systems, the distribution of off-diagonal matrix
elements is a gaussian centered at zero. As one approaches integrability, the
peak around zero becomes sharper, so that the distribution is approximately a
combination of two gaussians. We characterize the proximity to integrability
through the deviation of this distribution from a gaussian shape. We also
determine the scaling dependence on system size of the average magnitude of
off-diagonal matrix elements.Comment: 10 pages, 6 figure
Space-modulated Stability and Averaged Dynamics
In this brief note we give a brief overview of the comprehensive theory,
recently obtained by the author jointly with Johnson, Noble and Zumbrun, that
describes the nonlinear dynamics about spectrally stable periodic waves of
parabolic systems and announce parallel results for the linearized dynamics
near cnoidal waves of the Korteweg-de Vries equation. The latter are expected
to contribute to the development of a dispersive theory, still to come.Comment: Proceedings of the "Journ\'ees \'Equations aux d\'eriv\'ees
partielles", Roscoff 201
Constructive Wall-Crossing and Seiberg-Witten
We outline a comprehensive and first-principle solution to the wall-crossing
problem in D=4 N=2 Seiberg-Witten theories. We start with a brief review of the
multi-centered nature of the typical BPS states and recall how the
wall-crossing problem thus becomes really a bound state formation/dissociation
problem. Low energy dynamics for arbitrary collections of dyons is derived,
from Seiberg-Witten theory, with the proximity to the so-called marginal
stability wall playing the role of the small expansion parameter. We find that,
surprisingly, the low energy dynamics of n+1 BPS dyons cannot
be consistently reduced to the classical moduli space, \CM, yet the index can
be phrased in terms of \CM. We also explain how an equivariant version of
this index computes the protected spin character of the underlying field
theory, where SO(3)_\CJ isometry of \CM turns out to be the diagonal
subgroup of spatial rotation and R-symmetry. The so-called
rational invariants, previously seen in the Kontsevich-Soibelman formalism of
wall-crossing, are shown to emerge naturally from the orbifolding projection
due to Bose/Fermi statistics.Comment: 25 pages, conference proceeding contribution for "Progress of Quantum
Field Theory and String Theory," Osaka, April 201
Probing a topological quantum critical point in semiconductor-superconductor heterostructures
Quantum ground states on the non-trivial side of a topological quantum
critical point (TQCP) have unique properties that make them attractive
candidates for quantum information applications. A recent example is provided
by s-wave superconductivity on a semiconductor platform, which is tuned through
a TQCP to a topological superconducting (TS) state by an external Zeeman field.
Despite many attractive features of TS states, TQCPs themselves do not break
any symmetries, making it impossible to distinguish the TS state from a regular
superconductor in conventional bulk measurements. Here we show that for the
semiconductor TQCP this problem can be overcome by tracking suitable bulk
transport properties across the topological quantum critical regime itself. The
universal low-energy effective theory and the scaling form of the relevant
susceptibilities also provide a useful theoretical framework in which to
understand the topological transitions in semiconductor heterostructures. Based
on our theory, specific bulk measurements are proposed here in order to
characterize the novel TQCP in semiconductor heterostructures.Comment: 8+ pages, 5 figures, Revised version as accepted in PR
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