Equations-of-motion approach to a quantum theory of large-amplitude collective motion

The equations-of-motion approach to large-amplitude collective motion is implemented both for systems of coupled bosons, also studied in a previous paper, and for systems of coupled fermions. For the fermion case, the underlying formulation is that provided by the generalized Hartree-Fock approximation (or generalized density matrix method). To obtain results valid in the semi-classical limit, as in most previous work, we compute the Wigner transform of quantum matrices in the representation in which collective coordinates are diagonal and keep only the leading contributions. Higher-order contributions can be retained, however, and, in any case, there is no ambiguity of requantization. The semi-classical limit is seen to comprise the dynamics of time-dependent Hartree-Fock theory (TDHF) and a classical canonicity condition. By utilizing a well-known parametrization of the manifold of Slater determinants in terms of classical canonical variables, we are able to derive and understand the equations of the adiabatic limit in full parallelism with the boson case. As in the previous paper, we can thus show: (i) to zero and first order in the adiabatic limit the physics is contained in Villars' equations; (ii) to second order there is consistency and no new conditions. The structure of the solution space (discussed thoroughly in the previous paper) is summarized. A discussion of associated variational principles is given. A form of the theory equivalent to self-consistent cranking is described. A method of solution is illustrated by working out several elementary examples. The relationship to previous work, especially that of Zeievinsky and Marumori and coworkers is discussed briefly. Three appendices deal respectively with the equations-of-motion method, with useful properties of Slater determinants, and with some technical details associated with the fermion equations of motion.     

Dissipative quantum phase transition in a biased Tavis-Cummings model

We study the dissipative quantum phase transition(QPT)in a biased Tavis–Cummings model consisting of an ensemble of two-level systems(TLSs)interacting with a cavity mode,where the TLSs are pumped by a drive field.In our proposal,we use a dissipative TLS ensemble and an active cavity with effective gain.In the weak drive-field limit,the QPT can occur under the combined actions of the loss and gain of the system.Owing to the active cavity,the QPT behavior can be much differentiated even for a finite strength of the drive field on the TLS ensemble.Also,we propose to implement our scheme based on the dissipative nitrogen-vacancy(NV)centers coupled to an active optical cavity made from the gainmedium-doped silica.Furthermore,we show that the QPT can be measured by probing the transmission spectrum of the cavity embedding the ensemble of the NV centers.     

Continuous quantum phase transition in a Kndo lattice model

We study the magnetic quantum phase transition in an anisotropic Kondo lattice model. The dynamical competition between the RKKY and Kondo interactions is treated using an extended dynamic mean field theory appropriate for both the antiferromagnetic and paramagnetic phases. A quantum Monte Carlo approach is used, which is able to reach very low temperatures, of the order of 1% of the bare Kondo scale. We find that the finite-temperature magnetic transition, which occurs for sufficiently large RKKY interactions, is first order. The extrapolated zero-temperature magnetic transition, on the other hand, is continuous and locally critical.     

Dynamics of a quantum phase transition: exact solution of the quantum Ising model

The Quantum Ising model is an exactly solvable model of quantum phase transition. This Letter gives an exact solution when the system is driven through the critical point at a finite rate. The evolution goes through a series of Landau-Zener level anticrossings when pairs of quasiparticles with opposite pseudomomenta get excited with a probability depending on the transition rate. The average density of defects excited in this way scales like a square root of the transition rate. This scaling is the same as the scaling obtained when the standard Kibble-Zurek mechanism of thermodynamic second order phase transitions is applied to the quantum phase transition in the Ising model.     

A molecular quantum mechanics approach to evaluate molecular properties in liquid phase using statistical mechanics

A method for the calculation of molecular properties in liquid phase is proposed. The theoretical development links in a natural fashion Molecular Quantum Mechanics and Statistical Mechanics. The method can be applied to molecular liquids in thermodynamical equilibrium without strong interactions between molecules. After the Introduction (in which some fundamental ideas are discussed) the model is developed in its simplest form, giving a numerical application of interest for IR spectroscopy in liquid phase. Immediatly, this preliminar version is generalized for pure liquids taking into account the polarization effects on all the molecules of the sample. A numerical example on carbon disulphide shows the convergence of this method and its sensitivity to the structural changes in the liquid. In the last section, some future improvements are suggested and several topics related with the study of molecular liquids are considered.     

Symmetric transition probabilities in convex model of quantum mechanics

The relation between the geometry and the statistics of the quantum theory is most explicit in the convex models of quantum mechanics. A class of models is investigated where the manifold S of all states is a convex set with a smooth boundary. It is shown that for these models the simple assumption about symmetry of the transition probability implies an ellipsoidal shape of S, thus leading to the “spherical” geometries described in [7].     

On the quantum logic approach to quantum mechanics

A quantum logic structure for quantum mechanics which contains the concepts of a physical space, localizability, and symmetry groups is formulated. It is shown that there is an underlying Hilbert space which mirrors much of this axiomatic structure. Quantum fields are defined and shown to arise naturally from the quantum logic structure. The fields ofHaag andWightman are generalized to this theory and an attempt is made to find a local equivalence for these fields.     

A statistical approach to quantum mechanics

A Monte Carlo method is used to evaluate the Euclidean version of Feynman's sum over particle histories. Following Feynman's treatment, individual paths are defined on a discrete (imaginary) time lattice with periodic boundary conditions. On each lattice site, a continuous position variable x_i specifies the spacial location of the particle. Using a modified Metropolis algorithm, the low-lying energy eigenvalues, |ψ₀(x)|², the propagator, and the effective potential for the anharmonic oscillator are computed, in good agreement with theory. For a deep double-well potential, instantons were found in our computer simulations appearing as multi-kink configurations on the lattice.     

Nature of the quantum phase transition to a spin-nematic phase

It is shown that the quantum phase transition in metallic non-s-wave ferromagnets, or spin nematics, is generically of first order. This is due to a coupling of the order parameter to soft electronic modes that play a role analogous to that of the electromagnetic vector potential in a superconductor, which leads to a fluctuation-induced first-order transition. A generalized mean-field theory for the p-wave case is constructed that explicitly shows this effect. Tricritical wings are predicted to appear in the phase diagram in a spatially varying magnetic field, but not in a homogeneous one.     

Global quantum discord and quantum phase transition in XY model

We study the relationship between the behavior of global quantum correlations and quantum phase transitions in XY model. We find that the two kinds of phase transitions in the studied model can be characterized by the features of global quantum discord (GQD) and the corresponding quantum correlations. We demonstrate that the maximum of the sum of all the nearest neighbor bipartite GQDs is effective and accurate for signaling the Ising quantum phase transition, in contrast, the sudden change of GQD is very suitable for characterizing another phase transition in the XY model. This may shed lights on the study of properties of quantum correlations in different quantum phases.     

Breakdown of a topological phase: quantum phase transition in a loop gas model with tension

We study the stability of topological order against local perturbations by considering the effect of a magnetic field on a spin model--the toric code--which is in a topological phase. The model can be mapped onto a quantum loop gas where the perturbation introduces a bare loop tension. When the loop tension is small, the topological order survives. When it is large, it drives a continuous quantum phase transition into a magnetic state. The transition can be understood as the condensation of "magnetic" vortices, leading to confinement of the elementary "charge" excitations. We also show how the topological order breaks down when the system is coupled to an Ohmic heat bath and relate our results to error rates for topological quantum computations.     

Functional approach to scattering in quantum mechanics

A functional approach to scattering theory in quantum mechanics is developed by deriving an explicit functional expression fortransition amplitudes. In applications, the formalism avoids dealing with noncommutativity problems of operators, solving the Schrödinger equation (or the integral equation of the Green's function), or dealing with the often quite complicated continual (path) integrals and, most importantly, applies to short- and long-range interactions. The basic idea is the use of the quantum action principle followed by a systematic analysis of the concept of an intervening source developed earlier in the study of stimulated emission. A comparison with the standard approach is also made.     

Dynamics of a quantum phase transition

We present two approaches to the dynamics of a quench-induced phase transition in the quantum Ising model. One follows the standard treatment of thermodynamic second order phase transitions but applies it to the quantum phase transitions. The other approach is quantum, and uses Landau-Zener formula for transition probabilities in avoided level crossings. We show that predictions of the two approaches of how the density of defects scales with the quench rate are compatible, and discuss the ensuing insights into the dynamics of quantum phase transitions.     

Geometric phase and quantum phase transition in the one-dimensional compass model

We study the geometric phase of the ground state of the one-dimensional compass model in a transverse field. The critical properties of the system in terms of the geometric phase are calculated and discussed. The results show that the general character of quantum phase transitions (QPTs) in the model can be revealed by the Berry phase of the ground state. This study extends the relations between geometric phases and QPTs.     

Quantum chaos triggered by precursors of a quantum phase transition: the dicke model

We consider the Dicke Hamiltonian, a simple quantum-optical model which exhibits a zero-temperature quantum phase transition. We present numerical results demonstrating that at this transition the system changes from being quasi-integrable to quantum chaotic. By deriving an exact solution in the thermodynamic limit we relate this phenomenon to a localization-delocalization transition in which a macroscopic superposition is generated. We also describe the classical analogs of this behavior.     

Entanglement and quantum phase transition in the Heisenberg-Ising model

We use the quantum renormalization-group(QRG) method to study the entanglement and quantum phase transition(QPT) in the one-dimensional spin-1/2 Heisenberg-Ising model [Lieb E,Schultz T and Mattis D 1961 Ann.Phys.(N.Y.) 16 407].We find the quantum phase boundary of this model by investigating the evolution of concurrence in terms of QRG iterations.We also investigate the scaling behavior of the system close to the quantum critical point,which shows that the minimum value of the first derivative of concurrence and the position of the minimum scale with an exponent of the system size.Also,the first derivative of concurrence between two blocks diverges at the quantum critical point,which is directly associated with the divergence of the correlation length.