On the complexity of the k-customer vehicle routing problem

We investigate the complexity of the k-CUSTOMER VEHICLE ROUTING PROBLEM: Given an edge weighted graph, the problem requires to compute a minimum weight set of cyclic routes such that each contains a distinguished depot vertex and at most other k customer vertices, and every customer belongs to exactly one route.     

Phase transition in a system of one-dimensional bosons with strong disorder

We study one-dimensional disordered bosons at large commensurate filling. Using a real space renormalization group approach, we find a new random fixed point which controls a phase transition from a superfluid to an incompressible Mott glass. The transition can be tuned by changing the disorder distribution even with vanishing interactions. We derive the properties of the transition, which suggest that it is in the Kosterlitz-Thouless universality class.     

Who should be given priority in a queue?

We consider a memoryless single server queue with two classes of customers, each having its fixed entry fee. We show that profit and social welfare may benefit from a service discipline based on relative priorities.     

Topological Anderson insulator in three dimensions

We show that disorder, when sufficiently strong, can transform an ordinary metal with strong spin-orbit coupling into a strong topological "Anderson" insulator, a new topological phase of quantum matter in three dimensions characterized by disordered insulating bulk and topologically protected conducting surface states.     

Universal periods in quantum Hall droplets

Using the hierarchy picture of the fractional quantum Hall effect, we study the ground-state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is periodically modulated with flux through the droplet and will lead to a periodic variation in the conductance of a nearby point contact, such as occurs in some quantum Hall interferometers. Our model is consistent with experiment and predicts that superperiods can be observed in geometries where no interfering trajectories occur. The model may also provide an experimentally feasible method of detecting elusive neutral modes and otherwise obtaining information about the microscopic edge structure in fractional quantum Hall states.     

Superfluidity and magnetism in multicomponent ultracold fermions

We study the interplay between superfluidity and magnetism in a multicomponent gas of ultracold fermions. Ward-Takahashi identities constrain possible mean-field states describing order parameters for both pairing and magnetization. The structure of global phase diagrams arises from competition among these states as functions of anisotropies in chemical potential, density, or interactions. They exhibit first and second order phase transition as well as multicritical points, metastability regions, and phase separation. We comment on experimental signatures in ultracold atoms.     

Nash Equilibrium and Subgame Perfection in Observable Queues

A subgame perfection refinement of Nash equilibrium is suggested for games of the following type: each of an infinite number of identical players selects an action using his private information on the system's state; any symmetric strategy results in a discrete Markov chain over such states; the player's payoff is a function of the state, the selected action, and the common strategy selected by the other players. The distinction between equilibria which are subgame perfect and those which are not, is made apparent due to the possibility that some states are transient. We illustrate the concept by considering several queueing models in which the number of customers in the system constitutes the state of the system.     

Energy partitioning of tunneling currents into Luttinger liquids

Tunneling of electrons of definite chirality into a quantum wire creates counterpropagating excitations, carrying both charge and energy. We find that the partitioning of energy is qualitatively different from that of charge. The partition ratio of energy depends on the excess energy of the tunneling electrons (controlled by the applied bias) and on the interaction strength within the wire (characterized by the Luttinger-liquid parameter κ), while the partitioning of charge is fully determined by κ. Moreover, unlike for charge currents, the partitioning of energy current should manifest itself in dc experiments on wires contacted by conventional (Fermi-liquid) leads.