Vladislav Popkov

Empirical evidence for a boundary-induced nonequilibrium phase transition

A recently developed theory for boundary-induced phenomena in nonequilibrium systems predicts the existence of various steady-state phase transitions induced by the motion of a shock wave. We provide direct empirical evidence that a phase transition between a free flow and a congested phase occurring in traffic flow on highways in the vicinity of on- and off-ramps can be interpreted as an example of such a boundary-induced phase transition of first order. We analyse the empirical traffic data and give a theoretical interpretation of the transition in terms of the macroscopic current. Additionally we support the theory with computer simulations of the Nagel-Schreckenberg model of vehicular traffic on a road segment which also exhibits the expected second-order transition. Our results suggest ways to predict and to some extent to optimize the capacity of a general traffic network.

Symmetry breaking and phase coexistence in a driven diffusive two-channel system.

We consider classical hard-core particles moving on two parallel chains in the same direction. An interaction between the channels is included via the hopping rates. For a ring, the stationary state has a product form. For the case of coupling to two reservoirs, it is investigated analytically and numerically. In addition to the known one-channel phases, two new regions are found, in particular one, where the total density is fixed, but the filling of the individual chains changes back and forth, with a preference for strongly different densities. The corresponding probability distribution is determined and shown to have a universal form. The phase diagram and general aspects of the problem are discussed.

ASEP on a ring conditioned on enhanced flux

We show that in the asymmetric simple exclusion process (ASEP) on a ring, conditioned on carrying a large flux, the particle experiences an effective long-range potential which in the limit of very large flux takes the simple form , where n1, n2,..., nN are the particle positions, similar to the effective potential between the eigenvalues of the circular unitary ensemble in random matrices. Effective hopping rates and various quasi-stationary probabilities under such a conditioning are found analytically using the Bethe ansatz and determinantal free fermion techniques. Our asymptotic results extend to the limit of large current and large activity for a family of reaction–diffusion processes with on-site exclusion between particles. We point out an intriguing generic relation between classical stationary probability distributions for conditioned dynamics and quantum ground state wavefunctions, in particular in the case of exclusion processes, for free fermions.

Exactly solvable statistical model for two-way traffic

We generalize a recently introduced traffic model, where the statistical weights are associated with whole trajectories, to the case of two-way flow. An interaction between the two lanes is included which describes a slowing down when two cars meet. This leads to two coupled five-vertex models. It is shown that this problem can be solved by reducing it to two one-lane problems with modified parameters. In contrast to stochastic models, jamming appears only for very strong interaction between the lanes.

Dynamic phase transitions in electromigration-induced step bunching

Electromigration-induced step bunching in the presence of sublimation or deposition is studied theoretically in the attachment-limited regime. We predict a phase transition as a function of the relative strength of kinetic asymmetry and step drift. For weak asymmetry the number of steps between bunches grows logarithmically with bunch size, whereas for strong asymmetry at most a single step crosses between two bunches. In the latter phase the emission and absorption of steps is a collective process which sets in only above a critical bunch size and/or step interaction strength.

Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension

We obtain the exact solution of the one-loop mode-coupling equations for the dynamical structure function in the framework of non-linear fluctuating hydrodynamics in one space dimension for the strictly hyperbolic case where all characteristic velocities are different. All solutions are characterized by dynamical exponents which are Kepler ratios of consecutive Fibonacci numbers, which includes the golden mean as a limiting case. The scaling form of all higher Fibonacci modes are asymmetric Levy-distributions. Thus a hierarchy of new dynamical universality classes is established. We also compute the precise numerical value of the Prahofer-Spohn scaling constant to which scaling functions obtained from mode coupling theory are sensitive.

Anticoarsening and complex dynamics of step bunches on vicinal surfaces during sublimation.

A sublimating vicinal crystal surface can undergo a step bunching instability when the attachment-detachment kinetics is asymmetric, in the sense of a normal Ehrlich-Schwoebel effect. Here we investigate this instability in a model that takes into account the subtle interplay between sublimation and step-step interactions, which breaks the volume-conserving character of the dynamics assumed in previous work. On the basis of a systematically derived continuum equation for the surface profile, we argue that the nonconservative terms pose a limitation on the size of emerging step bunches. This conclusion is supported by extensive simulations of the discrete step dynamics, which show breakup of large bunches into smaller ones as well as arrested coarsening and periodic oscillations between states with different numbers of bunches.

Targeting pure quantum states by strong noncommutative dissipation

We propose a solution to the problem of realizing a predefined and arbitrary pure quantum state, based on the simultaneous presence of coherent and dissipative dynamics, noncommuting on the target state and in the limit of strong dissipation. More precisely, we obtain a necessary and sufficient criterion whereby the nonequilibrium steady state (NESS) of an open quantum system described by a Lindblad master equation approaches a target pure state in the Zeno regime, i.e., for infinitely large dissipative coupling. We also provide an explicit formula for the characteristic dissipative strength beyond which the purity of the NESS becomes effective, thus paving the way to an experimental implementation of our criterion. For an illustration, we deal with targeting a Bell state, an arbitrary pure state of

Solution of the Lindblad equation for spin helix states

N

Reduced density matrix and entanglement entropy of permutationally invariant quantum many-body systems

qubits, and a spin-helix state of