2,732 research outputs found
Non-commutative Nash inequalities
A set of functional inequalities - called Nash inequalities - are introduced
and analyzed in the context of quantum Markov process mixing. The basic theory
of Nash inequalities is extended to the setting of non-commutative Lp spaces,
where their relationship to Poincare and log-Sobolev inequalities are fleshed
out. We prove Nash inequalities for a number of unital reversible semigroups
Quantum logarithmic Sobolev inequalities and rapid mixing
A family of logarithmic Sobolev inequalities on finite dimensional quantum
state spaces is introduced. The framework of non-commutative \bL_p-spaces is
reviewed and the relationship between quantum logarithmic Sobolev inequalities
and the hypercontractivity of quantum semigroups is discussed. This
relationship is central for the derivation of lower bounds for the logarithmic
Sobolev (LS) constants. Essential results for the family of inequalities are
proved, and we show an upper bound to the generalized LS constant in terms of
the spectral gap of the generator of the semigroup. These inequalities provide
a framework for the derivation of improved bounds on the convergence time of
quantum dynamical semigroups, when the LS constant and the spectral gap are of
the same order. Convergence bounds on finite dimensional state spaces are
particularly relevant for the field of quantum information theory. We provide a
number of examples, where improved bounds on the mixing time of several
semigroups are obtained; including the depolarizing semigroup and quantum
expanders.Comment: Updated manuscript, 30 pages, no figure
How fast do stabilizer Hamiltonians thermalize?
We present rigorous bounds on the thermalization time of the family of
quantum mechanical spin systems known as stabilizer Hamiltonians. The
thermalizing dynamics are modeled by a Davies master equation that arises from
a weak local coupling of the system to a large thermal bath. Two temperature
regimes are considered. First we clarify how in the low temperature regime, the
thermalization time is governed by a generalization of the energy barrier
between orthogonal ground states. When no energy barrier is present the
Hamiltonian thermalizes in a time that is at most quadratic in the system size.
Secondly, we show that above a universal critical temperature, every stabilizer
Hamiltonian relaxes to its unique thermal state in a time which scales at most
linearly in the size of the system. We provide an explicit lower bound on the
critical temperature. Finally, we discuss the implications of these result for
the problem of self-correcting quantum memories with stabilizer Hamiltonians
Exciting the Rabble to Riots and Mobbing : Community, Public Rituals, and Popular Disturbances in Eighteenth-Century Virginia
Throughout the eighteenth century, Virginia\u27s populace acted in ways which reinforced the communal will. A deep rationality underlay popular action. While eighteenth-century contemporaries did not view it this way, historians must not view the mob as unruly. This thesis delineates the social laws displayed in the communal actions of pre-revolutionary Virginia, whether labeled by the elite as orderly or disorderly.
The Virginia Gazette and other sources during the quarter century before the Stamp Act show a society actively and publicly displaying communal and hierarchical values. Fairs reinforced the hierarchy through festive social interaction. Royal celebrations allowed the elite and populace to express communal as well as monarchical loyalty. Courthouse gatherings, more than any other social occasion, unified the community. Even contested elections, when resolved, often reinforced the hierarchical, yet consensual, community.
While society was not without tensions before 1765, disturbances increased when the Whig elite attempted to limit the British government\u27s political and economic influence. The Whig elite organized petitions and demonstrations against the Stamp Act, government agents, and merchants willing to conduct business under the new imperial laws. The Townshend Act further divided the Virginian elite into Patriots and Loyalists. Also in 1768 and 1769 an inoculation crisis divided the elite along the same lines. The inoculation riots were a product of both elite manipulation and customary beliefs.
The populace responded to these incidents by attempting to maintain community. While the root cause was Whig elite organization against British governmental officers or merchants, the forms taken in mob action and the victims chosen for public humiliation were distinctly popular: tar and feathering, ducking, burning in effigy, carting. Most riots were clearly orderly. Those people singled out by the mob for correction or humiliation either promoted individual (not community) interests or were viewed as community outsiders.
The implications of this study extend beyond 1775. Gordon S. Wood argues that the American Revolution was a radical social revolution. The evidence from colonial Virginia does suggest a breakdown of the consensual community view among the elite well before 1775. But this breakdown did not extend to the popular level. An analysis of popular rituals reveals the popular mentalité. Foremost in the popular eighteenth-century Virginia mind was the maintenance of community. Disorderly popular actions reinforced social stability and order
A Holographic Fractional Topological Insulator
We give a holographic realization of the recently proposed low energy
effective action describing a fractional topological insulator. In particular
we verify that the surface of this hypothetical material supports a fractional
quantum Hall current corresponding to half that of a Laughlin state.Comment: 4 pages, 2 figure
Exciting the Rabble to Riots and Mobbing : Community, Public Rituals, and Popular Disturbances in Eighteenth-Century Virginia
Throughout the eighteenth century, Virginia\u27s populace acted in ways which reinforced the communal will. A deep rationality underlay popular action. While eighteenth-century contemporaries did not view it this way, historians must not view the mob as unruly. This thesis delineates the social laws displayed in the communal actions of pre-revolutionary Virginia, whether labeled by the elite as orderly or disorderly.
The Virginia Gazette and other sources during the quarter century before the Stamp Act show a society actively and publicly displaying communal and hierarchical values. Fairs reinforced the hierarchy through festive social interaction. Royal celebrations allowed the elite and populace to express communal as well as monarchical loyalty. Courthouse gatherings, more than any other social occasion, unified the community. Even contested elections, when resolved, often reinforced the hierarchical, yet consensual, community.
While society was not without tensions before 1765, disturbances increased when the Whig elite attempted to limit the British government\u27s political and economic influence. The Whig elite organized petitions and demonstrations against the Stamp Act, government agents, and merchants willing to conduct business under the new imperial laws. The Townshend Act further divided the Virginian elite into Patriots and Loyalists. Also in 1768 and 1769 an inoculation crisis divided the elite along the same lines. The inoculation riots were a product of both elite manipulation and customary beliefs.
The populace responded to these incidents by attempting to maintain community. While the root cause was Whig elite organization against British governmental officers or merchants, the forms taken in mob action and the victims chosen for public humiliation were distinctly popular: tar and feathering, ducking, burning in effigy, carting. Most riots were clearly orderly. Those people singled out by the mob for correction or humiliation either promoted individual (not community) interests or were viewed as community outsiders.
The implications of this study extend beyond 1775. Gordon S. Wood argues that the American Revolution was a radical social revolution. The evidence from colonial Virginia does suggest a breakdown of the consensual community view among the elite well before 1775. But this breakdown did not extend to the popular level. An analysis of popular rituals reveals the popular mentalité. Foremost in the popular eighteenth-century Virginia mind was the maintenance of community. Disorderly popular actions reinforced social stability and order
More Holographic Berezinskii-Kosterlitz-Thouless Transitions
We find two systems via holography that exhibit quantum
Berezinskii-Kosterlitz-Thouless (BKT) phase transitions. The first is the ABJM
theory with flavor and the second is a flavored (1,1) little string theory. In
each case the transition occurs at nonzero density and magnetic field. The BKT
transition in the little string theory is the first example of a quantum BKT
transition in (3+1) dimensions. As in the "original" holographic BKT transition
in the D3/D5 system, the exponential scaling is destroyed at any nonzero
temperature and the transition becomes second order. Along the way we construct
holographic renormalization for probe branes in the ABJM theory and propose a
scheme for the little string theory. Finally, we obtain the embeddings and
(half of) the meson spectrum in the ABJM theory with massive flavor.Comment: 24 pages, 5 figure
Jets in strongly-coupled N = 4 super Yang-Mills theory
We study jets of massless particles in N=4 super Yang-Mills using the AdS/CFT
correspondence both at zero and finite temperature. We set up an initial state
corresponding to a highly energetic quark/anti-quark pair and follow its time
evolution into two jets. At finite temperature the jets stop after traveling a
finite distance, whereas at zero temperature they travel and spread forever. We
map out the corresponding baryon number charge density and identify the generic
late time behavior of the jets as well as features that depend crucially on the
initial conditions.Comment: 21 pages, 12 figures. Added discussion regarding string profiles in
more than one spatial dimension. Refs adde
Non-equilibrium dynamics of a Bose-Einstein condensate in an optical lattice
The dynamical evolution of a Bose-Einstein condensate trapped in a
one-dimensional lattice potential is investigated theoretically in the
framework of the Bose-Hubbard model. The emphasis is set on the
far-from-equilibrium evolution in a case where the gas is strongly interacting.
This is realized by an appropriate choice of the parameters in the Hamiltonian,
and by starting with an initial state, where one lattice well contains a
Bose-Einstein condensate while all other wells are empty. Oscillations of the
condensate as well as non-condensate fractions of the gas between the different
sites of the lattice are found to be damped as a consequence of the collisional
interactions between the atoms. Functional integral techniques involving
self-consistently determined mean fields as well as two-point correlation
functions are used to derive the two-particle-irreducible (2PI) effective
action. The action is expanded in inverse powers of the number of field
components N, and the dynamic equations are derived from it to next-to-leading
order in this expansion. This approach reaches considerably beyond the
Hartree-Fock-Bogoliubov mean-field theory, and its results are compared to the
exact quantum dynamics obtained by A.M. Rey et al., Phys. Rev. A 69, 033610
(2004) for small atom numbers.Comment: 9 pages RevTeX, 3 figure
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