Equilibrium superradiance in a Bose gas

A model of free₄He atoms interacting with radiation exhibits an equilibrium phase transition in which the atomic ground-state Bose condensation is coupled to condensations of virtual photons and virtually excited atoms of the same macroscopic wavelength. The condensed phase has a twofold polarization degeneracy. It is suggested that this might furnish a mechanism for a discrete symmetry-related phase degeneracy of superfluid liquid⁴He required to explain the transition according to Tisza's generalized Gibbsian thermodynamics. A more realistic model would require inclusion of repulsive interactions.Supported in part by the National Science Foundation, Grant DMR76-17467.     

Degeneracy of the ground-state of antiferromagnetic spin-1/2 Hamiltonians

In the first part of this paper, the extension of the Lieb-Schultz-Mattis theorem to dimensions larger than one is discussed. A counter example to the original formulation of Lieb-Schultz-Mattis and Affleck is exhibited and a more precise statement is formulated. The degeneracy of the ground-state in symmetry breaking phases with long-range order is analyzed. The second and third parts of the paper concern resonating valence-bond (RVB) spin liquids. In these phases the relationship between various authors approaches: Laughlin-Oshikawa, Sutherland, Rokhsar and Kivelson, Read and Chakraborty and the Lieb-Schultz-Mattis-Affleck proposal is studied. The deep physical relation between the degeneracy property and the absence of stiffness is explained and illustrated numerically. A new conjecture is formed concerning the absolute absence of sensitivity of the spin liquid ground-states to any twist of the boundary conditions (thermodynamic limit). In the third part of the paper the relations between the quantum numbers of the degenerate multiplets of the spin liquid phases are obtained exactly. Their relationship with a topological property of the wave functions of the low lying levels of this spin liquid phase is emphasized. In spite of the degeneracy of the ground-state, we explain why these phases cannot exhibit spontaneous symmetry breaking. Received 19 December 2001     

The open path phase for degenerate and non-degenerate systems and its relation to the wave-function modulus

We calculate the open path phase in a two state model with a slowly (nearly adiabatically) varying time-periodic Hamiltonian and trace its continuous development during a period. We show that the topological (Berry) phase attains π or 2π depending on whether there is or is not a degeneracy in the part of the parameter space enclosed by the trajectory. Oscillations are found in the phase. As adiabaticity is approached, these become both more frequent and less pronounced and the phase jump becomes increasingly more steep. Integral relations between the phase and the amplitude modulus (having the form of Kramers-Kronig relations, but in the time domain) are used as an alternative way to calculate open path phases. These relations attest to the observable nature of the open path phase.     

Discontinuous current-phase relations in small one-dimensional Josephson junction arrays

We study the Josephson effect in small one-dimensional (1D) Josephson junction arrays. For weak Josephson tunneling, topologically different regions in the charge-stability diagram generate distinct current-phase (I-phi) relationships. We present results for a three-junction system in the vicinity of charge-degeneracy lines and triple points. We explain the generalization to larger arrays, show that discontinuities of the I-phi relation at phase pi persist and that, at maximum degeneracy, the problem can be mapped to a tight-binding model providing analytical results for arbitrary system size.     

Two-dimensional periodic frustrated ising models in a transverse field

We investigate the interplay of classical degeneracy and quantum dynamics in a range of periodic frustrated transverse field Ising systems at zero temperature. We find that such dynamics can lead to unusual ordered phases and phase transitions or to a quantum spin liquid (cooperative paramagnetic) phase as in the triangular and kagome lattice antiferromagnets, respectively. For the latter, we further predict passage to a bond-ordered phase followed by a critical phase as the field is tilted. These systems also provide exact realizations of quantum dimer models introduced in studies of high temperature superconductivity.     

Collective dynamics of lipid membranes studied by inelastic neutron scattering

We have studied the collective short wavelength dynamics in deuterated 1,2-dimyristoyl-sn-glycero-3-phoshatidylcholine (DMPC) bilayers by inelastic neutron scattering. The corresponding dispersion relation variant Planck's over 2pi omega(Q) is presented for the gel and the fluid phase of this model system. The temperature dependence of the inelastic excitations indicates a phase coexistence between the two phases over a broad range and leads to a different assignment of excitations from that reported in a preceding inelastic x-ray scattering study [Phys. Rev. Lett. 86, 740 (2001)]]. As a consequence, we find that the minimum in the dispersion relation is actually deeper in the gel than in the fluid phase. Finally, we can clearly identify an additional nondispersive (optical) mode predicted by molecular dynamics simulations [Phys. Rev. Lett. 87, 238101 (2001)]].     

Non-linear diffusion in Hamiltonian systems exhibiting chaotic motion

The exact evolution equation for the angle averaged phase space density in action-angle space is derived from the Liouville equation using projection operator techniques. This equation involves a correlation function of the initial value of the phase space density with the angle dependent part of the Hamiltonian and a correlation function of the angle dependent part of the Hamiltonian and a correlation function of the angle dependent part of the Hamiltonian with itself. Each of these correlation functions develops in time with angle projected dynamics. We show their relation to the correlation functions which develop in time with usual Hamiltonian dynamics. These correlation functions are then studied in the standard model of Chirikov, and we conclude that they behave as $\text{e}{}^{\mathrm{-\sigma t}}\text{cos}\text{(Ωt + φ)}$ in regions of irregular motion. We conjecture that angle averaged correlation functions behave this way in general, and we give an argument based on the mixing property of the Hamiltonian system. Our argument goes beyond the usual mixing, so we regard it as a quasi-mixing hypothesis. Under this hypothesis the equation for the angle averaged phase space density becomes a diffusion equation which incorporates much of the non-linear dynamics of Hamiltonian systems exhibiting chaotic motion.     

Stable solution of the simplest spin model for inverse freezing

We analyze the Blume-Emery-Griffiths-Capel model with disordered interaction that displays the inverse freezing phenomenon. The behavior of this spin-1 model in crystal field is studied throughout the phase diagram, and the transition lines are computed using the full replica symmetry breaking ansatz. We compare the results both with the formulation of the same model in terms of Ising spins on lattice gas, where no reentrance takes place, and with the model with generalized spin variables recently introduced by Schupper and Shnerb [Phys. Rev. Lett. 93, 037202 (2004)], for which the reentrance is enhanced as the ratio between the degeneracy of full to empty sites increases. The simplest version of all these models, known as the Ghatak-Sherrington model, turns out to hold all the general features characterizing an inverse transition to an amorphous phase.     

Spectrum of the non-abelian phase in Kitaev’s honeycomb lattice model

The spectral properties of Kitaev’s honeycomb lattice model are investigated both analytically and numerically with the focus on the non-abelian phase of the model. After summarizing the fermionization technique which maps spins into free Majorana fermions, we evaluate the spectrum of sparse vortex configurations and derive the interaction between two vortices as a function of their separation. We consider the effect vortices can have on the fermionic spectrum as well as on the phase transition between the abelian and non-abelian phases. We explicitly demonstrate the 2ⁿ-fold ground state degeneracy in the presence of 2n well separated vortices and the lifting of the degeneracy due to their short-range interactions. The calculations are performed on an infinite lattice. In addition to the analytic treatment, a numerical study of finite size systems is performed which is in exact agreement with the theoretical considerations. The general spectral properties of the non-abelian phase are considered for various finite toroidal systems.     

An Anyon Model in a Toric Honeycomb Lattice

We study an anyon model in a toric honeycomb lattice. The ground states and the low-lying excitations coincide with those of Kitaev toric code model and then the excitations obey mutual semionic statistics. This model is helpful to understand the toric code of anyons in a more symmetric way. On the other hand, there is a direct relation between this toric honeycomb model and a boundary coupled Ising chain array in a square lattice via Jordan-Wignertransformation. We discuss the equivalence between these two modelsin the low-lying sector and realize these anyon excitations in a conventional fermion system. The analysis for the ground state degeneracy in the last section can also be thought of as a complementarity of our previous work [Phys. A: Math. Theor. 43 (2010) 105306].     

Creation, Dissipation and Recycling of Resources in Non-Equilibrium Systems

In this article, we define stochastic dynamics for a system coupled to reservoirs. The rules for forward and backward transitions are related by a generalized detailed balance identity involving the system and its reservoirs. We compare the variation of information and of entropy. We define the Carnot dissipation and prove that it can be expressed in terms of cyclic transformations. Lower bounds for partial dissipations are also studied, as well as the effect of switching off certain reservoirs. We also study the near degeneracy of the stochastic matrix, relate it to phase transitions and we show that the reduced dynamics on the set of phases is a permutation. Finally, we relate these concepts to heat, work and more generally to the dissipation and creation of resources, in general systems.     

Effective Interactions Due to Quantum Fluctuations

A class of quantum lattice models is considered, with Hamiltonians consisting of a classical (diagonal) part and a small off-diagonal part (e.g. hopping terms). In some cases when the classical part has an infinite degeneracy of ground states, the quantum perturbation may stabilize some of them. The mechanism of this stabilization stems from effective potential created by the quantum perturbation. Conditions are found when this strategy can be rigorously controlled and the low temperature phase diagram of the full quantum model can be proven to be a small deformation of the zero temperature phase diagram of the classical part with the effective potential added. As illustrations we discuss the asymmetric Hubbard model and the Bose–Hubbard model. Received: 28 April 1998 / Accepted: 19 March 1999     

s-channel discontinuities of reggeon diagrams with planar vertices

The mutual relations between s-channel discontinuities of reggeon diagrams with planar triple-Regge vertices are discussed. It is shown that, in general, contributions coming from different cuttings are not simply related to each other as certain vertices acquire non-trivial phase factors depending on the nature of the cutting. For diagrams with only triple-Regge vertices this phase may be related to the triple-Regge phase. The complete four-reggeon vertices are not known in general. An approximation is considered which amounts to preserving only the absorptive part of triple- or four-reggeon amplitudes in certain parts of the diagrams. This approximation turns out to be equivalent to a simple absorbed multiperipheral model. The problem of exchange degeneracy breaking within the dual unitarisation Scheme is briefly discussed as an example.     

On the Lorentz nature of confinement in heavy—light quarkonia

The Lorentz nature of the effective interquark interaction in a heavy—light quarkonium is studied using the vacuum correlators method and the generalized Nambu—Jona-Lasinio potential quark model. An effective scalar interaction is demonstrated to appear self-consistently owing to chiral-symmetry breaking and to dominate for low-lying states in the bound-state spectrum. The relation between such an effective interquark interaction and the QCD string approach is discussed. On the contrary, the upper part of this spectrum is found to be governed by the spatial Lorentz vector interaction which leads to a degeneracy for the states with opposite parity—the so-called restoration of chiral symmetry for excited hadrons. The text was submitted by the author in English.     

Equivalence of Non-equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model

We construct different equivalent non-equilibrium statistical ensembles in a simple yet instructive \(N\) -degrees of freedom model of atmospheric turbulence, introduced by Lorenz in 1996. The vector field can be decomposed into an energy-conserving, time-reversible part, plus a non-time reversible part, including forcing and dissipation. We construct a modified version of the model where viscosity varies with time, in such a way that energy is conserved, and the resulting dynamics is fully time-reversible. For each value of the forcing, the statistical properties of the irreversible and reversible model are in excellent agreement, if in the latter the energy is kept constant at a value equal to the time-average realized with the irreversible model. In particular, the average contraction rate of the phase space of the time-reversible model agrees with that of the irreversible model, where instead it is constant by construction. We also show that the phase space contraction rate obeys the fluctuation relation, and we relate its finite time corrections to the characteristic time scales of the system. A local version of the fluctuation relation is explored and successfully checked. The equivalence between the two non-equilibrium ensembles extends to dynamical properties such as the Lyapunov exponents, which are shown to obey to a good degree of approximation a pairing rule. These results have relevance in motivating the importance of the chaotic hypothesis. in explaining that we have the freedom to model non-equilibrium systems using different but equivalent approaches, and, in particular, that using a model of a fluid where viscosity is kept constant is just one option, and not necessarily the only option, for describing accurately its statistical and dynamical properties.     

The transfer matrix for a pure phase in the two-dimensional Ising model

The problem of diagonalizing the transfer matrix for the two dimensional Ising model with all boundary spins equal to +1 is solved by use of the spinor method. This provides a simple proof that the spontaneous magnetization is actually given by the well known formula for the long range order with torodial boundary conditions, and this means that the critical temperature is precisely that temperature above which the state is unique and below which it is non unique. An expression for the magnetization at finite distance from the boundary is also given, and a simple derivation of the formula for the surface tension between two coexisting phases is presented. Finally the relation between the degeneracy of the spectrum and the phase transition is discussed.     

Complex free energies and metastable lifetimes

For two simple models we consider the analytic continuation of the free energy across a first-order phase transition. For each system we also study an associated stochastic dynamics and decay rates for passage to the stable equilibrium. We then investigate the relation between the imaginary part of the free energy and the decay rate per unit volume.Supported in part by U.S.-Israel Binational Science Foundation and by National Science Foundation Grant MCS 77-20683.Alfred P. Sloan Research Fellow. On leave from Indiana University, Bloomington, Indiana.     

Spatial decoherence factor via the qubit-field interaction

We analyze the time evolution of an initial spatial coherence for a two level atom whose internal degrees of freedom interact with a single mode of a cavity field. When the qubit-field subsystem is taken as an environment, the translational dynamics experiences a decoherence process which may be encoded in a decoherence factor D. We find that the field statistics affects D through the alternative paths the system-environment may follow along their entanglement, while eventual field phase properties give rise to an imaginary part of D which is related to the atomic translation. From the decoherence perspective, we analyze the relation between the atomic momentum and the imaginary part of the atomic spatial density matrix, and some considerations on its asymptotic behavior are brought into question at the conclusion of the paper.