We present a comprehensive theoretical treatment of the effect of electron-phonon interactions on molecular transistors, including both quantal and classical limits. We study both equilibrated and out of equilibrium phonons. We present detailed results for conductance, noise and phonon distribution in two regimes. One involves temperatures large as compared to the rate of electronic transitions on and off the dot; in this limit our approach yields classical rate equations, which are solved numerically for a wide range of parameters. The other regime is that of low temperatures and weak electron-phonon coupling where a perturbative approximation in the Keldysh formulation can be applied. The interplay between the phonon-induced renormalization of the density of states on the quantum dot and the phonon-induced renormalization of the dot-lead coupling is found to be important. Whether or not the phonons are able to equilibrate in a time rapid compared to the transit time of an electron through the dot is found to affect the conductance. Observable signatures of phonon equilibration are presented. We also discuss the nature of the low-T to high-T crossover.

Graphene irradiated by a circularly polarized laser has been predicted to be a Floquet topological insulator showing a laser-induced quantum Hall effect. A circularly polarized laser also drives the system out of equilibrium resulting in non-thermal electron distribution functions that strongly affect transport properties. Results are presented for the Hall conductance for two different cases. One is for a closed system such as a cold-atomic gas where transverse drift due to non-zero Berry curvature can be measured in time of flight measurements. For this case the effect of a circularly polarized laser that has been switched on suddenly is studied. The second is for an open system coupled to an external reservoir of phonons. While for the former, the Hall conductance is far from the quantized limit, for the latter, coupling to a sufficiently low temperature reservoir of phonons is found to produce effective cooling, and thus an approach to the quantum limit, provided the frequency of the laser is large as compared to the band-width. For laser frequencies comparable to the band-width, strong deviations from the quantum limit of conductance is found even for a very low temperature reservoir, with the precise value of the Hall conductance determined by a competition between reservoir induced cooling and the excitation of photo-carriers by the laser. For the closed system, the electron distribution function is determined by the overlap between the initial wavefunction and the Floquet states which can result in a Hall conductance which is opposite in sign to that of the open system.

A theory is presented of quantum criticality in open (coupled to reservoirs) itinerant electron magnets, with nonequilibrium drive provided by current flow across the system. Both departures from equilibrium at conventional (equilibrium) quantum critical points and the physics of phase transitions induced by the nonequilibrium drive are treated. Nonequilibrium-induced phase transitions are found to have the same leading critical behavior as conventional thermal phase transitions.PACS numbers: 73.23.-b,05.30.-d,71.10-w,71.38.-k A central issue in condensed matter physics is the behavior of systems as one tunes parameters (for example pressure, or magnetic field) so as to change the symmetries characterizing the ground state [1,2,3,4]. The parameter values at which the ground state symmetries change (for example, from ferromagnetic metal to paramagnetic metal) define a quantum phase transition point (quantum critical point). At quantum phase transitions, spatial and temporal fluctuations are coupled, so that continuous quantum phase transitions in equilibrium systems are typically described by critical theories involving an effective dimensionality d eff greater than the spatial dimensionality d.While equilibrium quantum phase transitions have been extensively studied, the generalization to nonequilibrium conditions raises a largely open class of questions.Nonlinear transport near a superconductorinsulator phase transition [5,6] and a ferromagnetic transition driven by current flow in a closed one-dimensional system [7] have been studied; however, a general systematic understanding is lacking.In this paper we formulate a theory of nonequilibrium quantum criticality in itinerant electron systems coupled to reservoirs (c.f. upper panel of Fig. 1) with which particles may be exchanged. Nonequilibrium is imposed by differences between reservoirs; our systems are therefore subject to a time-independent drive, and are not characterized by any conserved quantities. A generic phase diagram is shown in the lower panel of Fig 1: we take a system which at temperature T = 0 may be tuned through an equilibrium quantum critical point by varying a parameter δ through a critical value δ c and determine the changes induced by a nonequilibrium drive (generically denoted as V ). Of particular interest is the transition generated by V if the V = 0 system is ordered (vertical arrow in lower panel of Fig. 1).Analysis of nonequilibrium systems proceeds from the time dependent density matrixρ(t) defined in terms of a HamiltonianĤ and an initial conditionρ(t init ) viâ ρ(t) = e −iĤ(t−tinit)ρ (t init )e iĤ (t−tinit) . The open systems we consider possess a well defined long-time state defined Schematic phase diagram in a plane of equilibrium distance from criticality, δ, and departure from equilibrium V . The quantum critical point δc separates the long range ordered (δ < δc) and disordered (δ > δc) phases. The solid line denotes a nonequilibrium phase transition. The dashed curves indicate the crossover from low V essentially equilibr...

Motivated by recent pump-probe spectroscopies, we study the effect of phonon dissipation and potential cooling on the nonequilibrium distribution function in a Floquet topological state. To this end, we apply a Floquet kinetic equation approach to study two dimensional Dirac fermions irradiated by a circularly polarized laser, a system which is predicted to be in a laser induced quantum Hall state. We find that the initial electron distribution shows an anisotropy with momentum dependent spin textures whose properties are controlled by the switching-on protocol of the laser. The phonons then smoothen this out leading to a non-trivial isotropic nonequilibrium distribution which has no memory of the initial state and initial switch-on protocol, and yet is distinct from a thermal state. An analytical expression for the distribution at the Dirac point is obtained that is relevant for observing quantized transport.

The non-equilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with O(N ) symmetry, starting from a ground state in the disordered phase. In the limit of infinite N , the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. Our analytical predictions are confirmed by the numerical solution of the corresponding equations. Moreover, we find that the same scaling functions, yet with different exponents, also describe the coarsening dynamics for quenches below the dynamical critical point.