Behavior Of Many-body Systems Research Articles

Mixing rate in Classical Many Body Systems

Mixing in many body systems is intuitively understood as the change in time of the set of neighbors surrounding each particle. Its rate and its development over time hold important clues to the behavior of many body systems. For example, gas particles constantly change their position and surrounding particles, while in solids one expects the motion of the atoms to be limited by a fixed set of neighboring atoms. In other systems the situation is less clear. For example, agitated granular systems may behave like a fluid, a solid or glass, depending on various parameter such as density and friction. Thus, we introduce a parameter which describes the mixing rate in many body systems in terms of changes of a properly chosen adjacency matrix. The parameter is easily measurable in simulations but not in experiment. To demonstrate an application of the concept, we simulate a many body system, with particles interacting via a two-body potential and calculate the mixing rate as a function of time and volume fraction. The time dependence of the mixing rate clearly indicates the onset of crystallization

Adiabatic State Preparation of Interacting Two-Level Systems

We consider performing adiabatic rapid passage (ARP) using frequency-swept driving pulses to excite a collection of interacting two-level systems. Such a model arises in a wide range of many-body quantum systems, such as cavity QED or quantum dots, where a nonlinear component couples to light. We analyze the one-dimensional case using the Jordan-Wigner transformation, as well as the mean-field limit where the system is described by a Lipkin-Meshkov-Glick Hamiltonian. These limits provide complementary insights into the behavior of many-body systems under ARP, suggesting our results are generally applicable. We demonstrate that ARP can be used for state preparation in the presence of interactions, and identify the dependence of the required pulse shapes on the interaction strength. In general, interactions increase the pulse bandwidth required for successful state transfer, introducing new restrictions on the pulse forms required.

Casimir invariants for systems undergoing collective motion

Dicke states are an important class of states which exhibit collective behavior in many-body systems. They are interesting because (1) the decay rates of these states can be quite different from a set of independently evolving particles and (2) a particular class of these states are decoherence-free or noiseless with respect to a set of errors. These noiseless states, or more generally subsystems, avoid certain types of errors in quantum-information-processing devices. Here we provide a method for determining a set of transformations of these states which leave the states in their subsystems but still enable them to evolve in particular ways. For subsystems of particles undergoing collective motions, these transformations can be calculated by using essentially the same construction which is used to determine the famous Casimir invariants for quantum systems. Such invariants can be used to determine a complete set of commuting observables for a class of Dicke states as well as to identify possible logical operations for decoherence-free--noiseless subsystems. Our method is quite general and provides results for cases where the constituent particles have more than two internal states.

Ultracold Fermionic Atoms Team up as Molecules: Can They Form Cooper Pairs as Well?

The behavior of strongly interacting degenerate Fermi gases may hold clues to the universal behavior of many-body systems.

On randomness and thermodynamics

The past decade has witnessed significant advances in our understanding of nonlinear systems, both theoretically and experimentally. In turn, these insights have led to applications over a broad range of subjects, as well as to new interpretations of complex behavior. Inevitably, it seems, there has been a concomitant rush to re-interpret various well-understood aspects of thermodynamic behavior in manybody systems by means of these mechanisms. It is perhaps useful, therefore, to examine these notions critically, and in doing so we are able to illuminate somewhat the origins of, and motivations for, various dubious descriptions of these systems. Among other things, one notices in such discussions an unfortunate focus on “randomness,” rather than on the actual role of probabilities in describing the phenomena. Although valuable insights into some areas of complex behavior have arisen from studies of so-called “deterministic chaos,” we can detect no influence they may have on the predictions of statistical mechanics, and thus conclude that they are of little relevance to the thermodynamic behavior of large systems.