7,392 research outputs found
Strong and weak thermalization of infinite non-integrable quantum systems
When a non-integrable system evolves out of equilibrium for a long time,
local observables are expected to attain stationary expectation values,
independent of the details of the initial state. However, intriguing
experimental results with ultracold gases have shown no thermalization in
non-integrable settings, triggering an intense theoretical effort to decide the
question. Here we show that the phenomenology of thermalization in a quantum
system is much richer than its classical counterpart. Using a new numerical
technique, we identify two distinct thermalization regimes, strong and weak,
occurring for different initial states. Strong thermalization, intrinsically
quantum, happens when instantaneous local expectation values converge to the
thermal ones. Weak thermalization, well-known in classical systems, happens
when local expectation values converge to the thermal ones only after time
averaging. Remarkably, we find a third group of states showing no
thermalization, neither strong nor weak, to the time scales one can reliably
simulate.Comment: 12 pages, 21 figures, including additional materia
Matrix Product States: Symmetries and Two-Body Hamiltonians
We characterize the conditions under which a translationally invariant matrix
product state (MPS) is invariant under local transformations. This allows us to
relate the symmetry group of a given state to the symmetry group of a simple
tensor. We exploit this result in order to prove and extend a version of the
Lieb-Schultz-Mattis theorem, one of the basic results in many-body physics, in
the context of MPS. We illustrate the results with an exhaustive search of
SU(2)--invariant two-body Hamiltonians which have such MPS as exact ground
states or excitations.Comment: PDFLatex, 12 pages and 6 figure
Resonating valence bond states in the PEPS formalism
We study resonating valence bond (RVB) states in the Projected Entangled Pair
States (PEPS) formalism. Based on symmetries in the PEPS description, we
establish relations between the toric code state, the orthogonal dimer state,
and the SU(2) singlet RVB state on the kagome lattice: We prove the equivalence
of toric code and dimer state, and devise an interpolation between the dimer
state and the RVB state. This interpolation corresponds to a continuous path in
Hamiltonian space, proving that the RVB state is the four-fold degenerate
ground state of a local Hamiltonian on the (finite) kagome lattice. We
investigate this interpolation using numerical PEPS methods, studying the decay
of correlation functions, the change of overlap, and the entanglement spectrum,
none of which exhibits signs of a phase transition.Comment: 11+9 pages, 28 figures. v2: More numerical results, and a few minor
improvements. v3: Accepted version (minor changes relative to v2),
Journal-Ref adde
Fundamental limitations in the purifications of tensor networks
We show a fundamental limitation in the description of quantum many-body
mixed states with tensor networks in purification form. Namely, we show that
there exist mixed states which can be represented as a translationally
invariant (TI) matrix product density operator (MPDO) valid for all system
sizes, but for which there does not exist a TI purification valid for all
system sizes. The proof is based on an undecidable problem and on the
uniqueness of canonical forms of matrix product states. The result also holds
for classical states.Comment: v1: 11 pages, 1 figure. v2: very minor changes. About to appear in
Journal of Mathematical Physic
Gapless Hamiltonians for the toric code using the PEPS formalism
We study Hamiltonians which have Kitaev's toric code as a ground state, and
show how to construct a Hamiltonian which shares the ground space of the toric
code, but which has gapless excitations with a continuous spectrum in the
thermodynamic limit. Our construction is based on the framework of Projected
Entangled Pair States (PEPS), and can be applied to a large class of
two-dimensional systems to obtain gapless "uncle Hamiltonians".Comment: 8 pages, 2 figure
Numerical Simulation of Nano Scanning in Intermittent-Contact Mode AFM under Q control
We investigate nano scanning in tapping mode atomic force microscopy (AFM)
under quality (Q) control via numerical simulations performed in SIMULINK. We
focus on the simulation of whole scan process rather than the simulation of
cantilever dynamics and the force interactions between the probe tip and the
surface alone, as in most of the earlier numerical studies. This enables us to
quantify the scan performance under Q control for different scan settings.
Using the numerical simulations, we first investigate the effect of elastic
modulus of sample (relative to the substrate surface) and probe stiffness on
the scan results. Our numerical simulations show that scanning in attractive
regime using soft cantilevers with high Qeff results in a better image quality.
We, then demonstrate the trade-off in setting the effective Q factor (Qeff) of
the probe in Q control: low values of Qeff cause an increase in tapping forces
while higher ones limit the maximum achievable scan speed due to the slow
response of the cantilever to the rapid changes in surface profile. Finally, we
show that it is possible to achieve higher scan speeds without causing an
increase in the tapping forces using adaptive Q control (AQC), in which the Q
factor of the probe is changed instantaneously depending on the magnitude of
the error signal in oscillation amplitude. The scan performance of AQC is
quantitatively compared to that of standard Q control using iso-error curves
obtained from numerical simulations first and then the results are validated
through scan experiments performed using a physical set-up
Mejora de las propiedades mecánicas y compatibilidad de mezclas de PHBV/PLA con plastificantes comerciales de origen bio
Actas del Congreso publicadas por ed. Compobell. ISBN 978-84-942655-8-7Mezclas de poli (3-hidroxibutirato-co-3-hidroxivalerato) (PHBV) y ácido poliláctico
(PLA) se prepararon con un plastificante comercial funcionalizado de origen bio. La
morfologĂa obtenida, asĂ como las propiedades mecánicas y dinamo-mecánicas de
probetas inyectadas se ha evaluado observándose una mejora en la compatibilidad del
PHBV y el PLA y un aumento en la deformaciĂłn a rotura en tracciĂłn.A number of samples of poly (3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) and polylactic acid (PLA) were treated with a commercial funcionalised bio plasticiser. The relevant assessment was made on the morphology and both the mechanic and dynamo-mechanic properties obtained in the injected test tubes. An improvement in terms of compatibility between PHBV and PLA has been observed, as well as an increase in strain at break in tensile testing.Ministerio de EconomĂa y Competitividad (proyecto MAT2012-38947-C02-01) y Pla de PromociĂł de la InvestigaciĂł de la Universitat Jaume I (PREDOC / 2012/32
Adjoint fermion zero-modes for SU(N) calorons
We derive analytic formulas for the zero-modes of the Dirac equation in the
adjoint representation in the background field of Q=1 SU(N) calorons. Solutions
with various boundary conditions are obtained, including the physically most
relevant cases of periodic and antiperiodic ones. The latter are essential
ingredients in a semiclassical treatment of finite temperature supersymmetric
Yang-Mills theory. A detailed discussion of adjoint zero-modes in several other
contexts is also presented.Comment: 40 latex pages and 5 eps figure
Decoherence and relaxation in the interacting quantum dot system
In this paper we study the low temperature kinetics of the electrons in the
system composed of a quantum dot connected to two leads by solving the equation
of motion. The decoherence and the relaxation of the system caused by the gate
voltage noise and electron-phonon scattering are investigated. In order to take
account of the strong correlation of the electrons in this system, the
quasi-exact wave functions are calculated using an improved matrix product
states algorithm. This algorithm enables us to calculate the wave functions of
the ground state and the low lying excited states with satisfied accuracy and
thus enables us to study the kinetics of the system more effectively. It is
found that although both of these two mechanisms are proportional to the
electron number operator in the dot, the kinetics are quite different. The
noise induced decoherence is much more effective than the energy relaxation,
while the energy relaxation and decoherence time are of the same order for the
electron-phonon scattering. Moreover, the noise induced decoherence increases
with the lowering of the dot level, but the relaxation and decoherence due to
the electron-phonon scattering decrease.Comment: Minor revision. Add journal referenc
Quantum kinetic Ising models
We introduce a quantum generalization of classical kinetic Ising models,
described by a certain class of quantum many body master equations. Similarly
to kinetic Ising models with detailed balance that are equivalent to certain
Hamiltonian systems, our models reduce to a set of Hamiltonian systems
determining the dynamics of the elements of the many body density matrix. The
ground states of these Hamiltonians are well described by matrix product, or
pair entangled projected states. We discuss critical properties of such
Hamiltonians, as well as entanglement properties of their low energy states.Comment: 20 pages, 4 figures, minor improvements, accepted in New Journal of
Physic
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