18,836 research outputs found
Geometry of system-bath coupling and gauge fields in bosonic ladders: manipulating currents and driving phase transitions
Quantum systems in contact with an environment display a rich physics
emerging from the interplay between dissipative and Hamiltonian terms. Here we
focus on the role of the geometry of the coupling between the system and the
baths. In the specific we consider a dissipative boundary driven ladder in
presence of a gauge field which can be implemented with ion microtraps arrays.
We show that, depending on the geometry, the currents imposed by the baths can
be strongly affected by the gauge field resulting in non-equilibrium phase
transitions. In different phases both the magnitude of the current and its
spatial distribution are significantly different. These findings allow for
novel strategies to manipulate and control transport properties in quantum
systems.Comment: 8 pages, 4 figures, accepted in Phys. Rev.
Localization of Rota-Baxter algebras
A commutative Rota-Baxter algebra can be regarded as a commutative algebra
that carries an abstraction of the integral operator. With the motivation of
generalizing the study of algebraic geometry to Rota-Baxter algebra, we extend
the central concept of localization for commutative algebras to commutative
Rota-Baxter algebras. The existence of such a localization is proved and, under
mild conditions, its explicit constructions are obtained. The existence of
tensor products of commutative Rota-Baxter algebras is also proved and the
compatibility of localization and tensor product of Rota-Baxter algebras is
established. We further study Rota-Baxter coverings and show that they form a
Gr\"othendieck topology.Comment: 19 page
Indoor Frame Recovery from Refined Line Segments
An important yet challenging problem in understanding indoor scene is
recovering indoor frame structure from a monocular image. It is more difficult
when occlusions and illumination vary, and object boundaries are weak. To
overcome these difficulties, a new approach based on line segment refinement
with two constraints is proposed. First, the line segments are refined by four
consecutive operations, i.e., reclassifying, connecting, fitting, and voting.
Specifically, misclassified line segments are revised by the reclassifying
operation, some short line segments are joined by the connecting operation, the
undetected key line segments are recovered by the fitting operation with the
help of the vanishing points, the line segments converging on the frame are
selected by the voting operation. Second, we construct four frame models
according to four classes of possible shooting angles of the monocular image,
the natures of all frame models are introduced via enforcing the cross ratio
and depth constraints. The indoor frame is then constructed by fitting those
refined line segments with related frame model under the two constraints, which
jointly advance the accuracy of the frame. Experimental results on a collection
of over 300 indoor images indicate that our algorithm has the capability of
recovering the frame from complex indoor scenes.Comment: 39 pages, 11 figure
Matrix Product States with adaptive global symmetries
Quantum many body physics simulations with Matrix Product States can often be
accelerated if the quantum symmetries present in the system are explicitly
taken into account. Conventionally, quantum symmetries have to be determined
before hand when constructing the tensors for the Matrix Product States
algorithm. In this work, we present a Matrix Product States algorithm with an
adaptive symmetry. This algorithm can take into account of, or benefit
from, or symmetries when they are present, or analyze the
non-symmetric scenario when the symmetries are broken without any external
alteration of the code. To give some concrete examples we consider an XYZ model
and show the insight that can be gained by (i) searching the ground state and
(ii) evolving in time after a symmetry-changing quench. To show the generality
of the method, we also consider an interacting bosonic system under the effect
of a symmetry-breaking dissipation.Comment: 9 pages, 4 figure
Dissipatively driven strongly interacting bosons in a gauge field
The interplay between dissipation, interactions and gauge fields opens the
possibility to rich emerging physics. Here we focus on a set-up in which the
system is coupled at its extremities to two different baths which impose a
current. We then study the system's response to a gauge field depending on the
filling. We show that while the current induced by the baths has a marked
dependence on the magnetic field at low fillings which is significantly reduced
close to half-filling. We explain the interplay between interactions, gauge
field and dissipation by studying the system's energy spectrum at the different
fillings. This interplay also results in the emergence of negative differential
conductivity. For this study we have developed a number-conserving treatment
which allows a numerical exact treatment of fairly large system sizes, and
which can be extended to a large class of systems.Comment: 5 pages, 5 figure
Guaranteed Classification via Regularized Similarity Learning
Learning an appropriate (dis)similarity function from the available data is a
central problem in machine learning, since the success of many machine learning
algorithms critically depends on the choice of a similarity function to compare
examples. Despite many approaches for similarity metric learning have been
proposed, there is little theoretical study on the links between similarity
met- ric learning and the classification performance of the result classifier.
In this paper, we propose a regularized similarity learning formulation
associated with general matrix-norms, and establish their generalization
bounds. We show that the generalization error of the resulting linear separator
can be bounded by the derived generalization bound of similarity learning. This
shows that a good gen- eralization of the learnt similarity function guarantees
a good classification of the resulting linear classifier. Our results extend
and improve those obtained by Bellet at al. [3]. Due to the techniques
dependent on the notion of uniform stability [6], the bound obtained there
holds true only for the Frobenius matrix- norm regularization. Our techniques
using the Rademacher complexity [5] and its related Khinchin-type inequality
enable us to establish bounds for regularized similarity learning formulations
associated with general matrix-norms including sparse L 1 -norm and mixed
(2,1)-norm
Fast and Strong Convergence of Online Learning Algorithms
In this paper, we study the online learning algorithm without explicit
regularization terms. This algorithm is essentially a stochastic gradient
descent scheme in a reproducing kernel Hilbert space (RKHS). The polynomially
decaying step size in each iteration can play a role of regularization to
ensure the generalization ability of online learning algorithm. We develop a
novel capacity dependent analysis on the performance of the last iterate of
online learning algorithm. The contribution of this paper is two-fold. First,
our nice analysis can lead to the convergence rate in the standard mean square
distance which is the best so far. Second, we establish, for the first time,
the strong convergence of the last iterate with polynomially decaying step
sizes in the RKHS norm. We demonstrate that the theoretical analysis
established in this paper fully exploits the fine structure of the underlying
RKHS, and thus can lead to sharp error estimates of online learning algorithm
Tuning energy transport using interacting vibrational modes
We study energy transport in a chain of quantum harmonic and anharmonic
oscillators where the anharmonicity is induced by interaction between local
vibrational states of the chain. Using adiabatic elimination and numerical
simulations with matrix product states, we show how strong interactions
significantly slow down the relaxation dynamics (with the emergence of a new
time scale) and can alter the properties of the steady state. We also show that
steady state properties are completely different depending on the order in
which the limits of infinite time and infinite interaction are taken.Comment: 5+3 pages. 6 figure
Interplay of interaction and disorder in the steady state of an open quantum system
Many types of dissipative processes can be found in nature or be engineered,
and their interplay with a system can give rise to interesting phases of
matter. Here we study the interplay among interaction, tunneling, and disorder
in the steady state of a spin chain coupled to a tailored bath. We consider a
dissipation which, in contrast to disorder, tends to generate a homogeneously
polarized steady state. We find that the steady state can be highly sensitive
even to weak disorder. We also establish that, in the presence of such
dissipation, even in the absence of interaction, a finite amount of disorder is
needed for localization. Last, we show that for strong disorder the system
reveals signatures of localization both in the weakly and strongly interacting
regimes.Comment: 5 pages, 5 figure
Semidefinite representations of non-compact convex sets
We consider the problem of the semidefinite representation of a class of
non-compact basic semialgebraic sets. We introduce the conditions of
pointedness and closedness at infinity of a semialgebraic set and show that
under these conditions our modified hierarchies of nested theta bodies and
Lasserre's relaxations converge to the closure of the convex hull of .
Moreover, if the PP-BDR property is satisfied, our theta body and Lasserre's
relaxation are exact when the order is large enough; if the PP-BDR property
does not hold, our hierarchies convergent uniformly to the closure of the
convex hull of restricted to every fixed ball centered at the origin. We
illustrate through a set of examples that the conditions of pointedness and
closedness are essential to ensure the convergence. Finally, we provide some
strategies to deal with cases where the conditions of pointedness and
closedness are violated.Comment: 25 pages, 9 figure
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