Norm-overlap formula for Hartree-Fock-Bogoliubov states with odd number parity

A formula to calculate the norm overlap between Hartree-Fock-Bogoliubov (HFB) states with odd number parity (one quasi-particle excited states) is derived with the help of Grassmann numbers and Fermion coherent states. The final formula is expressed in terms of a product of the Pfaffian for a neighboring even-even system (the zero quasi-particle state), and an extra factor consisting of the Bogoliubov transformation matrix and the anti-symmetric matrix in Thouless? HFB ansatz for the even-even system.     

SPINOR MONOPOLE SOLUTION IS POSSIBLE

By introducing a direct scalar coupling between the spinor field and the Higgs field, we are able to show that in the non-abelian case, a spinor monopole bound state solution exists. The distribution of the spinor field in the solution concentrates near the origin, which is unlike the shell distribution of the SLAC solution.     

A BOSON-FERMION DESCIPTION OF THE NUCLEAR MANY-BODY PROBLEM

A new formalism of the nuclear many-body problem is established in which one ean work with various physical state vector spaces consisting of both Fermions and Bosons, all being equivalent to the original one consisting only of Fermions.With the help of the usual commutation relations and anticommutation relations between the annihilation and creation operators of Boson and Fermion, a generalized state vector space is established, which contains all the physical spaces each being equivalent to the original physical space in terms of pure Fermion operators. Transformation between the state vectors in various equivalent physical spaces are constructed. Basic operators in the original state space are transformed into effective operators in the new physical spaces.     

Rayleigh-Schrödinger-Goldstone variational perturbation theory for many Fermion systems

We present a Rayleigh-Schrödinger-Goldstone perturbation formalism for many Fermion systems. Based on this formalism, variational perturbation scheme which goes beyond the Gaussian approximation is developed. In order to go beyond the Gaussian approximation, we identify a parent Hamiltonian which has an effective Gaussian vacuum as a variational solution and carry out further perturbation with respect to the renormalized interaction using Goldstones expansion. Perturbation rules for the ground state wavefunctional and energy are found, thus, opening a way for general use of the Schrödinger picture method for many Fermion systems. Useful commuting relations between operators and the Gaussian wavefunctional are also found, which could reduce the calculational efforts substantially. As examples, we calculate the first order correction to the Gaussian wavefunctional and the second order correction to the ground state of an electron gas system with the Yukawa-type interaction.     

Permion spectrum in a confined SU(n) quark model

An explicit form of a colour-singlet Fermion field is constructed from the operator solution of SU(n) Thirring model where the quark-fields are known to be confined in LSZ sense. In simple cases of massless quarks these ferions are free with zero mass and can be expressed as the antisymmetric composites of constituent quark fields. This simple exercise suggests an alternative to conventional two-dimensional QCD which seems to confine all Fermion including baryons by Schwinger mechanism.     

The lattice Schwinger model with SLAC fermions

The lattice Schwinger model with SLAC fermions is analyzed with two methods: a Hartree-Fock calculation of the ground state wave function, and a weak coupling approximation involving a truncated SLAC derivative. It is shown that a Goldstone boson of chiral symmetry is actually present, but in the weak coupling limit it acquires infinite velocity.     

Schwinger-Dyson equation for massless vector theory and the absence of a fermion pole

The Schwinger-Dyson equation of the fermion propagator in the massless vector theory is discussed. It is found that the Baker-Johnson-Willey solution in lowest approximation is in fact a confining solution: the Fermion propagator has no pole or cut in the time-like region. Discussions of homogeneous and inhomogeneous equations with momentum integration cut-off are also given in some detail.     

Practical application of cross correlation technique to measure jitter of master-oscillator-power-amplifier (MOPA) laser system

The Linac coherent light source (LCLS) at the SLAC National Accelerator Laboratory (SLAC) is the world’s first hard X-ray free electron laser (XFEL) and is capable of producing high-energy, femtosecond duration X-ray pulses. A common technique to study fast timescale physical phenomena, various “pump/probe” techniques are used. In these techniques there are two lasers, one optical and one X-ray, that work as a pump and as a probe to study dynamic processes in atoms and molecules. In order to resolve phenomena that occur on femtosecond timescales, it is imperative to have very precise timing between the optical lasers and X-rays (on the order of ～20 fs or better). The lasers are synchronized to the same RF source that drives the accelerator and produces the X-ray laser. However, elements in the lasers cause some drift and time jitter, thereby de-synchronizing the system. This paper considers cross-correlation technique as a way to quantify the drift and jitter caused by the regenerative amplifier of the ultrafast optical laser.     

Coherent X-ray diffraction radiation produced by microbunched beams passing close to the edge of a slab

With use of formulas for single-particle X-ray transition and diffraction radiation (XTR and XDR), we obtain expressions for spectral-angular distributions and total numbers of emitted quanta in coherent X-ray transition radiation (CXTR2) and coherent X-ray diffraction radiation (CXDR) arising when a microbunched beam of electrons, respectively, intersects the interfaces of a slab or flies at small distance from the edge of the slab. Comparison of obtained results with those known for CXTR from a single interface is performed. It is shown on the basis of numerical calculations that experimental study of CXDR is at present possible on the Linac Coherent Light Source (LCLS, SLAC).     

Coherence and squeezing in Z3‐graded spin coherent states

A new kind of spin coherent state called a Z₃‐graded spin coherent state is constructed by using the complex solution of the equation q³ = 1. We explicitly find three kinds of Z₃‐graded spin coherent states. The associated coherent property and spin squeezing are also examined.     

Joint Extension of States of Subsystems for a CAR System

 The problem of existence and uniqueness of a state of a joint system with given restrictions to subsystems is studied for a Fermion system, where a novel feature is non-commutativity between algebras of subsystems. For an arbitrary (finite or infinite) number of given subsystems, a product state extension is shown to exist if and only if all states of subsystems except at most one are even (with respect to the Fermion number). If the states of all subsystems are pure, then the same condition is shown to be necessary and sufficient for the existence of any joint extension. If the condition holds, the unique product state extension is the only joint extension. For a pair of subsystems, with one of the given subsystem states pure, a necessary and sufficient condition for the existence of a joint extension and the form of all joint extensions (unique for almost all cases) are given. For a pair of subsystems with non-pure subsystem states, some classes of examples of joint extensions are given where non-uniqueness of joint extensions prevails. Received: 17 May 2002 / Accepted: 16 January 2003 Published online: 17 April 2003 Communicated by D. Buchholz and K.Fredenhagen     

Ground states of Fermions on lattices

We consider Fermion systems on integer lattices. We establish the existence of dynamics for a class of long range interactions. The infinite volume ground states are considered. The equivalence of the variational principle and ground state conditions is proved for long range interactions. We also prove that any pure translationally invariant ground state of the gauge invariant algebra is extendible to a ground state of the full CAR algebra for the Hamiltonian with a chemical potential (equivalence of ensemble for canonical and ground canonical states at the zero temperature).     

Interactions of condensate atoms in the process of velocity-selective coherent population trapping

The properties of a one-dimensional atomic Bose condensate are studied under the assumption that the condensation leads to a state of velocity-selective coherent population trapping. This state is characterized by the quantum correlation (entanglement) between the intrinsic angular momentum of an atom and its translational motion underlying nontrivial features of the condensate. The effects of weak interatomic interaction are taken into account. The steady state of above-condensate atoms corresponding to the slow decay of the state with coherent population trapping is found. The dynamic problem concerning the evolution of the system of above-condensate atoms after switching off the optical field forming the state with coherent population trapping is solved. The solution is found by the diagonalization of the Hamiltonian based on introducing the Bogoliubov quasiparticles with the unusual dispersion law.     

The Stability of the Non-Equilibrium Steady States

We show that the non-equilibrium steady state (NESS) of the free lattice Fermion model far from equilibrium is macroscopically unstable. The problem is translated to that of the spectral analysis of the Liouville Operator. We use the method of positive commutators to investigate it. We construct a positive commutator on the lattice Fermion system, whose dispersion relation is (k)=cosk–.     

Unification of fermion and Boson stochastic calculus

Fermion annihilation and creation processes are explicitly realised in Boson Fock space as functions of the corresponding Boson processes and second quantisations of reflections. Conversely, Boson annihilation and creation processes can be constructed from the Fermion processes. The existence of unitary stochastic evolutions driven by Fermion and gauge noise is thereby reduced to an equivalent Boson problem, which is then solved.This work was carried out while both authors were participating in the Symposium on Stochastic Differential Equations at the University of Warwick. The first author acknowledges conversations with R.F. Streater during the same Symposium     

Wigner function and phase properties for a two-qubit field system under pure phase noise

We investigate an analytical solution for a two-qubit field system in the dispersive regime with a reservoir. We analyze the influence of the phase damping on the Wigner function and the phase properties. We found that the phase damping destroys the phase probability of the global system for the coherent state and even coherent state. The phase damping leads to decay of the Wigner function for the coherent state.     

载流子与铁磁物质耦合系统的严格对角化解与相干态变分方法

引用Schwinger的角动量谐振子理论将载流子与铁磁物质耦合系统变换为载流子与两类玻色子耦合的问题，对铁磁物质中束缚极化子的存在决定于介质中有无杂质势的规律进行了严格对角化求解. 得到的结论与普遍的看法一致，与相干态变分方法计算的基态能结果十分吻合，两种方法得到的波矢定性上也吻合，说明了相干态变分方法的可靠性和有较高的准确性，严格对角化解方法也可为其他的近似方法提供检验基础.     

Schwinger boson mapping of SO(8) fermion model

The Schwinger representation of the SO(8) fermion pair algebra in terms ofd and quasispin vector (u, s, v) bosons is used in deriving a microscopic boson coherent state having both particle-hole and pair excitations. The coherent state is the exact boson image of the HFB variational solution. We can study the shape phase transition and pairing behaviour of the nuclear ground states using the coherent states.