Concept Of Off-diagonal Long-range Order Research Articles

Kramers–Kronig Relations for the Dielectric Permittivity of the Coulomb System with a Single-Species Bose–Einstein Condensate

Using the linear response theory and the concept of off-diagonal long-range order, the Kramers–Kronig relations for the dielectric permittivity of a disordered Coulomb system in the presence of a single-component Bose–Einstein condensate for nuclei are obtained.

Correlation Dynamics of Dipolar Bosons in 1D Triple Well Optical Lattice

The concept of spontaneous symmetry breaking and off-diagonal long-range order (ODLRO) are associated with Bose–Einstein condensation. However, as in the system of reduced dimension the effect of quantum fluctuation is dominating, the concept of ODLRO becomes more interesting, especially for the long-range interaction. In the present manuscript, we study the correlation dynamics triggered by lattice depth quench in a system of three dipolar bosons in a 1D triple-well optical lattice from the first principle using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). Our main motivation is to explore how ODLRO develops and decays with time when the system is brought out-of-equilibrium by a sudden change in the lattice depth. We compare results of dipolar bosons with contact interaction. For forward quench ( V f > V i ) , the system exhibits the collapse–revival dynamics in the time evolution of normalized first- and second-order Glauber’s correlation function, time evolution of Shannon information entropy both for the contact as well as for the dipolar interaction which is reminiscent of the one observed in Greiner’s experiment [Nature, 415 (2002)]. We define the collapse and revival time ratio as the figure of merit ( τ ) which can uniquely distinguish the timescale of dynamics for dipolar interaction from that of contact interaction. In the reverse quench process ( V i > V f ) , for dipolar interaction, the dynamics is complex and the system does not exhibit any definite time scale of evolution, whereas the system with contact interaction exhibits collapse–revival dynamics with a definite time-scale. The long-range repulsive tail in the dipolar interaction inhibits the spreading of correlation across the lattice sites.

Bardeen–Cooper–Schrieffer (BCS) theory and Yang's concept of off-diagonal long-range order (ODLRO)

In this contribution, we pay tribute to the scientific achievements of Professor Rodney J. Bartlett on account of his seminal contributions to the many-body electron correlation problem. We are here concerned with strongly correlated situations as met in the theory of superconductivity. In condensed matter physics, one often makes use of the famous Bardeen–Cooper–Schrieffer (BCS) formulation, while quantum chemists often instigate an approach that originates in Yang's concept of off-diagonal long-range order (ODLRO), and the Coleman–Sasaki extreme state. Our aim is to demonstrate that both approaches are essentially equivalent by deriving the BCS gap equation from the assumption of the presence of ODLRO.

The Ubiquity of Superconductivity

After a brief review of the phenomenology of superconductivity and of its generic explanation in terms of the concept of off-diagonal long-range order, I first survey the original Bardeen-Cooper-Schrieffer (BCS) weak-coupling model and some extensions of it. I then turn to systems such as the heavy fermions and the cuprates where the superconductivity is generally believed to be due to an all-electronic mechanism, and ask how much information we get about this mechanism from quite general energetic and other considerations, without committing ourselves to any particular microscopic model.

Odd-parity triplet pair induced by Hund's rule coupling.

We discuss microscopic aspects of the odd-parity triplet pair in orbital degenerate systems. From the concept of off-diagonal long-range order, a pair state is unambiguously defined as the eigenstate with the maximum eigenvalue of a pair correlation function. Performing this scheme by a numerical technique, we clarify that the odd-parity triplet pair occurs as an out-of-phase combination of local triplets induced by Hund's rule coupling for the lattice including two sites in the unit cell.

Construction of a microscopic model forf-electron systems on the basis of aj−jcoupling scheme

We construct a microscopic model for f-electron systems, composed of f-electron hopping, Coulomb interaction, and crystalline electric field (CEF) terms. In order to clarify the meaning of one f-electron state, here the j-j coupling scheme is considered, since the spin-orbit interaction is generally large in f-electron systems. Thus, the f-electron state at each site is labelled by $\mu$, namely, the z-component of total angular momentum j. By paying due attention to f-orbital symmetry, the hopping amplitudes between f-electron states are expressed using Slater's integrals. The Coulomb interaction terms among the $\mu$-states are written by Slater-Condon or Racah parameters. Finally, the CEF terms are obtained from the table of Hutchings. The constructed Hamiltonian is regarded as an orbital degenerate Hubbard model, since it includes two pseudo-spin and three pseudo-orbital degrees of freedom. For practical purposes, it is further simplified into a couple of two-orbital models by discarding one of the three orbitals. One of those simplified models is here analyzed using the exact diagonalization method to clarify ground-state properties by evaluating several kinds of correlation functions. Especially, the superconducting pair correlation function in orbital degenerate systems is carefully calculated based on the concept of off-diagonal long-range order. We attempt to discuss a possible relation of the present results with experimental observations for recently discovered heavy fermion superconductors CeMIn$_5$ (M=Ir, Co, and Rh), and a comprehensive scenario to understand superconducting and antiferromagnetic tendencies in the so-called ``115'' materials such as CeMIn$_5$, UMGa$_5$, and PuCoGa$_5$ from the microscopic viewpoint.

Reduced density-matrix equations and superfluid hydrodynamics

A theory is developed which shows explicitly how Bose condensation leads to the phenomenological theory of superfluidity. Starting with the concept of off-diagonal long-range order for the reduced one-particle density matrix for an interacting Bose system, a closed set of hydrodynamic equations for the condensate and the depletion is derived. Viscous terms are not included. This set of equations is used to construct the hydrodynamic conservation laws. From a systematic comparison with Landau's phenomenological theory simple analytic connections between the densities and the velocities of the microscopic and the phenomenological theories are obtained. The validity of these relations is limited to low densities and to temperatures near Tλ. An explicit expression for the transition rate between the super and the normal component is given, and all thermodynamical functions are calculated. From the equation of motion for the condensate wave function an equation for the thermodynamical order parameter is derived which is valid in the vicinity of Tλ.

Hydrodynamic Equations for the Condensate and the Depletion of Helium II

The equations of motion for the reduced density matrices of an interacting Bose system are treated using the concept of off-diagonal long-range order. The equations are decoupled on the one-particle level. With this approximation, the hydrodynamic equations for the densities and the velocities of the condensate and the depletion are derived. The interaction between the two fluid components depends on density variations and on the relative velocity. The latter interaction terms appear as kinetic pressure terms and a Magnus force term. Via the equation for the total momentum, a connection between the velocities of the condensate and the depletion, and the velocities in Landau's two-fluid model is derived. The excitation spectrum of the system is investigated in the phonon region. A comparison of the resulting velocities for the first and second sound with the experimentally determined ones shows that the functional dependence of the condensate density on temperature is similar to that of the superfluid component.

Theory of Superfluidity

A new structure for the microscopic theory of superfluid helium is presented which is motivated by analogy with radiation of ideal lasers and with the BCS theory of superconductivity. The concept of off-diagonal long-range order is employed to put these three phenomena on a common basis. The unifying concept is that the ground state is that which completely factors the reduced density matrix appropriate to the basic group. It is shown how the model predicted by this motivation can also be derived from the microscopic Hamiltonian by a quasiparticle self-consistent-field approximation. The superfluid ground state can be viewed as energy-lowering coherent excitations of the normal fluid. The normal and superfluid components are the direct analog of noise and signal in partially radiation fields.

Concept of Off-Diagonal Long-Range Order and the Quantum Phases of Liquid He and of Superconductors

This review is concerned with the concept that in a many-body system of bosons or fermions, it is possible to have an off-diagonai long-range order of the reduced density matrices in the coordinate space representation. The onset of such an order ieads to a new thermodynamic phase of the system. It is reasonabie to assume that superfluid He II and the superconductors are phases characterized by the existence of such an order. (W.D.M.)