Anatoli Polkovnikov

Dynamical quantum phase transitions in the transverse-field Ising model.

A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to nonanalytic behavior of the free energy density at the critical temperature: The knowledge of the free energy density in one phase is insufficient to predict the properties of the other phase. In this Letter we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely nonanalytic behavior at a critical time. We denote such behavior a dynamical phase transition and explore its properties in the transverse-field Ising model. Specifically, we show that the equilibrium quantum phase transition and the dynamical phase transition in this model are intimately related.

Phase space representation of quantum dynamics

Abstract We discuss a phase space representation of quantum dynamics of systems with many degrees of freedom. This representation is based on a perturbative expansion in quantum fluctuations around one of the classical limits. We explicitly analyze expansions around three such limits: (i) corpuscular or Newtonian limit in the coordinate–momentum representation, (ii) wave or Gross–Pitaevskii limit for interacting bosons in the coherent state representation, and (iii) Bloch limit for the spin systems. We discuss both the semiclassical (truncated Wigner) approximation and further quantum corrections appearing in the form of either stochastic quantum jumps along the classical trajectories or the nonlinear response to such jumps. We also discuss how quantum jumps naturally emerge in the analysis of non-equal time correlation functions. This representation of quantum dynamics is closely related to the phase space methods based on the Wigner–Weyl quantization and to the Keldysh technique. We show how such concepts as the Wigner function, Weyl symbol, Moyal product, Bopp operators, and others automatically emerge from the Feynmanns path integral representation of the evolution in the Heisenberg representation. We illustrate the applicability of this expansion with various examples mostly in the context of cold atom systems including sine-Gordon model, one- and two-dimensional Bose–Hubbard model, Dicke model and others.

AUGER RECOMBINATION IN SEMICONDUCTOR QUANTUM WELLS

The principal mechanisms of Auger recombination of nonequilibrium carriers in semiconductor heterostructures with quantum wells are investigated. It is shown for the first time that there exist three fundamentally different Auger recombination mechanisms of (i) thresholdless, (ii) quasi-threshold, and (iii) threshold types. The rate of the thresholdless Auger process depends on temperature only slightly. The rate of the quasi-threshold Auger process depends on temperature exponentially. However, its threshold energy essentially varies with quantum well width and is close to zero for narrow quantum wells. It is shown that the thresholdless and the quasi-threshold Auger processes dominate in narrow quantum wells, while the threshold and the quasi-threshold processes prevail in wide quantum wells. The limiting case of a three-dimensional (3D)Auger process is reached for infinitely wide quantum wells. The critical quantum well width is found at which the quasi-threshold and threshold Auger processes merge into a single 3D Auger process. Also studied is phonon-assisted Auger recombination in quantum wells. It is shown that for narrow quantum wells the act of phonon emission becomes resonant, which in turn increases substantially the coefficient of phonon-assisted Auger recombination. Conditions are found under which the direct Auger process dominates over the phonon-assisted Auger recombination at various temperatures and quantum well widths.

Threshold characteristics of InGaAsP/InP multiple quantum well lasers

A theoretical analysis and computer simulation of the threshold current density jth and characteristic temperature T0 of multiple quantum well lasers (MQWLs) are presented. Together with the spontaneous radiative recombination, the Auger recombination and the lateral diffusive leakage of carriers from the active region are included into the model. A first-principle calculation of the Auger recombination current is performed. It is shown that the lateral diffusive leakage current is controlled by the radiative and Auger currents. When calculating the carrier densities, the electrons in the barrier regions are properly taken into account. Redistribution of electrons over the active region is shown to increase the threshold current considerably. The dependences of jth and T0 on temperature, number of QWs, cavity length and lateral size are discussed in detail. The effect of lattice and carrier heating on jth and T0 is investigated and shown to be essential at high temperature.

Universal adiabatic dynamics in the vicinity of a quantum critical point

We study temporal behavior of a quantum system under a slow external perturbation, which drives the system across a second-order quantum phase transition. It is shown that despite the conventional adiabaticity conditions are always violated near the critical point, the number of created excitations still goes to zero in the limit of infinitesimally slow variation of the tuning parameter. It scales with the adiabaticity parameter as a power related to the critical exponents

Impurity in a d-Wave Superconductor: Kondo Effect and STM Spectra

z

Many-body energy localization transition in periodically driven systems

and

Interference between independent fluctuating condensates

ensuremath{nu}

Full quantum distribution of contrast in interference experiments between interacting one-dimensional Bose liquids

characterizing the phase transition. We support general arguments by direct calculations for the Boson Hubbard and the transverse field Ising models.

Observation of topological transitions in interacting quantum circuits

We present a theory for recent STM studies of Zn impurities in the superconductor Bi2Sr2CaCu2O8+delta, using insights from NMR experiments which show that there is a net S = 1/2 moment on the Cu ions near the Zn. We argue that the Kondo spin dynamics of this moment is the origin of the low bias peak in the differential conductance, rather than a resonance in a purely potential scattering model. The spatial and energy dependence of the STM spectra of our model can also fit the experiments.