Strongly correlated fermions after a quantum quench

Using the adaptive time-dependent density-matrix renormalization group method, we study the time evolution of strongly correlated spinless fermions on a one-dimensional lattice after a sudden change of the interaction strength. For certain parameter values, two different initial states (e.g., metallic and insulating) lead to observables which become indistinguishable after relaxation. We find that the resulting quasistationary state is nonthermal. This result holds for both integrable and nonintegrable variants of the system.     

Quantum relaxation after a quench in systems with boundaries

We study the time dependence of the magnetization profile, m(l)(t), of a large finite open quantum Ising chain after a quench. We observe a cyclic variation, in which starting with an exponentially decreasing period the local magnetization arrives to a quasistationary regime, which is followed by an exponentially fast reconstruction period. The nonthermal behavior observed at near-surface sites turns over to thermal behavior for bulk sites. In addition to the standard time and length scales a nonstandard time scale is identified in the reconstruction period.     

Mode-coupling-induced dissipative and thermal effects at long times after a quantum quench

An interaction quench in a Luttinger liquid can drive it into an athermal steady state. We analyze the effects on such an out of equilibrium state of a mode coupling term due to a periodic potential. Employing a perturbative renormalization group approach we show that even when the periodic potential is an irrelevant perturbation in equilibrium, it has important consequences on the athermal steady state as it generates a temperature as well as a dissipation and hence a finite lifetime for the bosonic modes.     

Time dependence of correlation functions following a quantum quench

We show that the time dependence of correlation functions in an extended quantum system in d dimensions, which is prepared in the ground state of some Hamiltonian and then evolves without dissipation according to some other Hamiltonian, may be extracted using methods of boundary critical phenomena in d + 1 dimensions. For d = 1 particularly powerful results are available using conformal field theory. These are checked against those available from solvable models. They may be explained in terms of a picture, valid more generally, whereby quasiparticles, entangled over regions of the order of the correlation length in the initial state, then propagate classically through the system.     

Nonequilibrium work equalities in isolated quantum systems

We briefly introduce the quantum Jarzynski and Bochkov–Kuzovlev equalities in isolated quantum Hamiltonian systems, including their origin, their derivations using a quantum Feynman–Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, and recent experimental verifications. Some results are given here for the first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which are useful for understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.     

Defect production in nonlinear quench across a quantum critical point

We show that the defect density n, for a slow nonlinear power-law quench with a rate tau(-1) and an exponent alpha>0, which takes the system through a critical point characterized by correlation length and dynamical critical exponents nu and z, scales as n approximately tau(-alphanud/(alphaznu+1)) [n approximately (alphag((alpha-1)/alpha)/tau)(nud/(znu+1))] if the quench takes the system across the critical point at time t=0 [t=t(0) not = 0], where g is a nonuniversal constant and d is the system dimension. These scaling laws constitute the first theoretical results for defect production in nonlinear quenches across quantum critical points and reproduce their well-known counterpart for a linear quench (alpha=1) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.     

Entropy of nonrotating isolated horizons in Lovelock theory from loop quantum gravity

In this paper,the BF theory method is applied to the nonrotating isolated horizons in Lovelock theory.The final entropy matches the Wald entropy formula for this theory.We also confirm the conclusion obtained by Bodendorfer et al.that the entropy is related to the flux operator rather than the area operator in general diffeomorphic-invariant theory.     

Exact infinite-time statistics of the Loschmidt echo for a quantum quench

The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this Letter we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small quenches in the opposite, quasicritical regime, the distribution function acquires a universal double-peaked form indicating poor equilibration. These findings, obtained by a central limit theorem-type result, extend to completely general models in the small-quench regime.     

Many-body dynamics of exciton creation in a quantum dot by optical absorption: a quantum quench towards Kondo correlations

We study a quantum quench for a semiconductor quantum dot coupled to a fermionic reservoir, induced by the sudden creation of an exciton via optical absorption. The subsequent emergence of correlations between spin degrees of freedom of dot and reservoir, culminating in the Kondo effect, can be read off from the absorption line shape and understood in terms of the three fixed points of the single-impurity Anderson model. At low temperatures the line shape is dominated by a power-law singularity, with an exponent that depends on gate voltage and, in a universal, asymmetric fashion, on magnetic field, indicative of a tunable Anderson orthogonality catastrophe.     

Nonthermal statistics in isolated quantum spin clusters after a series of perturbations

We show numerically that a finite isolated cluster of interacting spins 1/2 exhibits a surprising nonthermal statistics when subjected to a series of small nonadiabatic perturbations by an external magnetic field. The resulting occupations of energy eigenstates are significantly higher than the thermal ones on both the low and the high ends of the energy spectra. This behavior semiquantitatively agrees with the statistics predicted for the so-called "quantum microcanonical" ensemble, which includes all possible quantum superpositions with a given energy expectation value. Our findings also indicate that the eigenstates of the perturbation operators are generically localized in the energy basis of the unperturbed Hamiltonian. This kind of localization possibly protects the thermal behavior in the macroscopic limit.     

Entropy production and its positivity in nonlinear response theory of quantum dynamical systems

A formulation ofentropy production is given with the aid of relative entropy in the nonlinear response theory of a quantum dynamical system. It allows a natural interpretation of the quantity in terms of familiar thermodynamic notions, such as force and response current conjugate to it, without sacrificing the full nonlinearity in the perturbing force. For the understanding ofdissipativity aspositive entropy production, the stationarity of states and coarse graining of time scale turn out to be essential, which are implemented by some time averaging procedures involvingalmost periodic external forces. Finally, it is shown that the obtained result reduces, in the linear response regime, to the power dissipation appearing in the well-known fluctuation-dissipation relation.     

Entropy,information and Maxwell’s demon after quantum mechanics

The problem of the subjective nature of entropy and its relation to information and irreversibility is examined in the light of the quantum measurement problem. The main thesis of the paper is that state collapse during a measurement and hence entropy increase in the observed universe is seen by observers who are only able to observe a restricted manifold of states determined by their concepts, language, etc., in short by their level of perception. The thesis leads to the assertion that any universe with a structure must evolve.     

Entropy in quantum ratchet for a delta-kicked model

We investigate the evolution of Shannon entropy in quantum ratchet effect for a delta-kicked model, where a particle with initial momentum zero is periodically kicked by an asymmetric potential. It is shown that the evolution of Shannon entropy of the particle can remarkably reflect whether quantum resonance emerges and gives rise to ratchet current or not. Furthermore, for different kinds of quantum resonances, low-order or high-order quantum resonances, the evolutions of the entropy are quite different.     

Effect of rare fluctuations on the thermalization of isolated quantum systems

We consider the question of thermalization for isolated quantum systems after a sudden parameter change, a so-called quantum quench. In particular, we investigate the prerequisites for thermalization, focusing on the statistical properties of the time-averaged density matrix and of the expectation values of observables in the final eigenstates. We find that eigenstates, which are rare compared to the typical ones sampled by the microcanonical distribution, are responsible for the absence of thermalization of some infinite integrable models and play an important role for some nonintegrable systems of finite size, such as the Bose-Hubbard model. We stress the importance of finite size effects for the thermalization of isolated quantum systems and discuss two scenarios for thermalization.     

Quantum phases and dynamics of geometric phase in a quantum spin chain under linear quench

We study the quantum phases of anisotropic XY spin chain in presence and absence of adiabatic quench. A connection between geometric phase and criticality is established from the dynamical behavior of the geometric phase for a quench induced quantum phase transition in a quantum spin chain. We predict XX criticality associated with a sequence of non-contractible geometric phases.     

Entropy,information and quantum measurements

The conditional entropy between two states of a quantum system is shown to be nonincreasing when a complete measurement is performed on the system. The information between two quantum systems is defined and is shown to be bounded above by the logarithmic correlation. This inequality is then applied to the measurement process. The entropy changes in the observed system and the measuring apparatus are compared with the information gain in the measurement.     

Entropy and irreversibility for a single isolated two level system: New individual quantum states and new nonlinear equation of motion

We propose a new nonlinear equation of motion for a single isolated two-level quantum system. The resulting generalized two-level quantum dynamical theory entails a new alternative resolution of the long-standing dilemma on the nature of entropy and irreversibility. Even for a single isolated degree of freedom, in addition to the individual mechanical states for which all the results of conventional quantum mechanics remain valid, our theory implies the existence of new nonmechanical individual quantum states. These states have nonzero individual entropy and, by virtue of a constant-energy, internal redistribution mechanism, relax irreversibly toward stable equilibrium. We discuss the possibility of an experimental verification of these conclusions by means of a high-resolution, essentially single-particle, magnetic-resonance experiment.     

Dynamics of the geometric phase in the adiabatic limit of a quench induced quantum phase transition

The geometric phase associated with a many body ground state exhibits a signature of quantum phase transition. In this context, we have studied the behavior of the geometric phase during a linear quench caused by a gradual turning off of the magnetic field interacting with a spin chain.