Beta function and anomaly of the Fermi surface for a d=1 system of interacting fermions in a periodic potential

We derive a perturbation theory, based on the renormalization group, for the Fermi surface of a one dimensional system of fermions in a periodic potential interacting via a short range, spin independent potential. The infrared problem is studied by writing the Schwinger functions in terms of running couplings. Their flow is described by a Beta function, whose existence and analyticity as a function of the running couplings is proved. If the fermions are spinless we prove that the Beta function is vanishing and the renormalization flow is bounded for any small interaction. If the fermions are spinning the Beta function is not vanishing but, if the conduction band is not filled or half filled and the interaction is repulsive, it is possible again to control the flow proving the partial asymptotic freedom of the theory. This is done showing that the Beta function is partially vanishing using the exact solution of the Mattis model, which is the spin analogue of the Luttinger model. In both these cases Schwinger functions are anomalous so that the system is a Luttinger liquid. Our results extend the work in [B.G.P.S.], where neither spin nor periodic potential were considered; an explicit proof of some technical results used but not explicitly proved there is also provided.     

On the Density-Density Critical Indices¶in Interacting Fermi Systems

The behaviour of correlation functions of d=1$ interacting fermionic systems is determined by a small number of critical indices. We prove that one of them is exactly zero. As a consequence, the behavior of the Fourier transform of the density-density correlation at zero momentum is qualitatively unaffected by the interaction, contrary to what happens at , if is the Fermi momentum. The result is obtained by implementing Ward identities in a Renormalization Group approach. Received: 12 November 2001 / Accepted: 25 February 2002?Published online: 2 October 2002     

1+1维非线性σ模型的BRST变换的等价性和Ward恒等式

在依据Dirac约束规范理论和作推广后的条件下,导出了规范生成元,推导出了1+1维O(3)非线性σ模型的一般条件(β≠0)下的BRST变换,给出了其BRST变换与Dirac规范变换的等价关系,得到了鬼场的新的一般对易关系,且其一般参数β为零时就回到通常的鬼场的对易关系.并由规范生成元导出了BRST荷,进而完成了此模型的一种BRST量子化.还在此基础上进一步导出了此系统的Green函数生成泛函、连通Green函数生成泛函和正规顶角生成泛函,获得了3种不同的Ward恒等式     

Singularities in the Vertex Function in Two-Dimensional Tight-Binding Fermi Systems

The singularities in the vertex function are studied within the ladder approximation for a non-half-filled two-dimensional tight- binding Fermi system. The location of all the possible poles of the vertex function has been clarified for both repulsive and attractive interacting cases.. The scattering phase shift is examined and found not always zero at Fermi energy. The Kohn-lut tinger-like singularity is also briefly discussed.     

Ward Identities and Chiral Anomaly in the Luttinger Liquid

Systems of interacting non-relativistic fermions in d =1, as well as spin chains or interacting two dimensional Ising models, verify an hidden approximate Gauge invariance which can be used to derive suitable Ward identities. Despite the presence of corrections and anomalies, such Ward identities can be implemented in a Renormalization Group approach and used to exploit nontrivial cancellations which allow to control the flow of the running coupling constants; in particular this is achieved combining Ward identities, Dyson equations and suitable correction identities for the extra terms appearing in the Ward identities, due to the presence of cutoffs breaking the local gauge symmetry. The correlations can be computed and show a Luttinger liquid behavior characterized by non-universal critical indices, so that the general Luttinger liquid construction for one dimensional systems is completed without any use of exact solutions. The ultraviolet cutoff can be removed and a Quantum Field Theory corresponding to the Thirring model is also constructed.     

Thermal Entanglement for Interacting Spin-1/2 Systems and its Quantum Criticality

In this work, we investigate the thermal entanglement for interacting spin systems , by varying the parameters of temperature T, direction and magnetic field B. PACS numbers: 03.67.Mn, 03.65.Ud, 05.30.Cd, 73.43.Nq     

Cluster Expansion for Ideal Fermi Systems in the “Fixed Node Approximation”

Results of the direct path integral Monte Carlo simulation (DPIMCS) have shown that the “fixed node approximation” (FNA) rather well describes thermodynamic properties of the strongly coupled fermions at “weak and moderate” degeneracy. To explain the increasing difference for highly degenerate fermions it is rigorously proved that the exact Fermi function with index 5/2 in grand ensemble can not be reproduced in FNA, so FNA has not the correct limit to ideal fermions.     

Fermi surface of 3d1 perovskite CaVO3 near the Mott transition

We present a detailed de Haas-van Alphen effect study of the perovskite CaVO3, offering an unprecedented test of electronic structure calculations in a 3d transition metal oxide. Our experimental and calculated Fermi surfaces are in good agreement, but only if we ignore large orthorhombic distortions of the cubic perovskite structure. Subtle discrepancies may shed light on an apparent conflict between the low energy properties of CaVO3, which are those of a simple metal, and high energy probes which reveal strong correlations that place CaVO3 on the verge of a metal-insulator transition.     

Quantum Locality for a Pair of Interacting Systems

We discuss the quantum locality （non-transfer of information） for a pair of mutually interacting systems, and point out the relaxed locality. The models fulfilling the relaxed locality condition can serve as a guide for quantum engineers in designing quantum-information hardware.     

Nonequilibrium Relaxation of Bose-Einstein Condensates: Real-Time Equations of Motion and Ward Identities

We present a field-theoretical method to obtain consistently the equations of motion for small amplitude condensate perturbations in a homogeneous Bose-condensed gas directly in real time. It is based on a linear response and combines the Schwinger-Keldysh formulation of nonequilibrium quantum field theory with the Nambu-Gor'kov formalism of quasiparticle excitations in the condensed phase and the tadpole method in quantum field theory. This method leads to causal equations of motion that allow us to study the nonequilibrium evolution as an initial value problem. It also allows us to extract directly the Ward identities, which are a consequence of the underlying gauge symmetry and which in equilibrium lead to the Hugenholtz-Pines theorem. An explicit one-loop calculation of the equations of motion beyond the Hartree-Fock-Bogoliubov approximation reveals that the nonlocal, absorptive contributions to the self-energies corresponding to the Beliaev and Landau damping processes are necessary to fulfill the Ward identities in or out of equilibrium. It is argued that a consistent implementation at low temperatures must be based on the loop expansion, which is shown to fulfill the Ward identities order by order in perturbation theory.     

N = 3 and N = 1 supersymmetry in a new class of solutions for d = 11 supergravity

We present a new class of compactifying solutions for d = 11 supergravity. The internal 7-spaces are described by coset manifolds N^pqr of the form SU(3) × U(1)/U(1) × U(1). The three integers p, q, r characterize the embedding of the stability subgroup U(1) × U(1) in SU(3) × U(1).Their supersymmetry content is quite remarkable. For a particular choice of p, q, r the isometry of N^pqr is SU(3) × SU(2): in this case we find that N = 3 supersymmetry survives. For all the other values of p, q, r, supersymmetry is broken to N = 1, and the isometry group is SU(3) × U(1).We also find a class of solutions with internal photon curl F_αβγδ ≠ 0, breaking all supersymmetries.     

相互作用体系的极化率与拉曼光谱

分子的大多数光学性能取决于它的极化率和超极化率，例如折射率、旋光、Ｒａｙｌｅｉｇｈ和Ｒａｍａｎ散射、电光、磁光和非线性光学性能等［１］。分子间相互作用对于物质的性质有着深刻影响［２］，对于分子极化率及其有关的性能也是如此３］。本文在拉曼光谱强度理论（...     

On the Nature of Fermi Golden Rule for Open Quantum Systems

We consider a general class of models consisting of a small quantum system $S$ interacting with a reservoir $R$ . We compare three applications of 2nd order perturbation theory (the Fermi Golden Rule) to the study of such models: (1) the van Hove (weak coupling) limit for the dynamics reduced to $S$ ; (2) the Fermi Golden Rule applied to the Liouvillean—an argument that was used in recent papers on the return to equilibrium; (3) the Fermi Golden Rule applied to the so-called C-Liouvillean. These three applications lead to three Level Shift Operators. As our main result, we prove that if the reservoir $R$ is thermal (if it satisfies the KMS condition), then the Level Shift Operator obtained in (1) (often called the Davies generator) and the Level Shift Operator constructed in (2) are connected by a similarity transformation. We also show that the Davies generator coincides with the Level Shift Operator obtained in (3) for a general $R$ .     

Extended Theory of Finite Fermi Systems for magic and nonmagic nuclei

Consideration is given to a short review of the main features, recent results, and prospects of the Extended Theory of Finite Fermi Systems (ETFFS), which has been applied in the past 15 years to collective excitations in the neutral channel for nuclei with and without pairing. The theory is an extension of the Migdal standard TFFS to include in a consistent way the single-particle continuum and more complex 1p1h ⊗ phonon or 2qp ⊗ phonon configurations beyond the RPA or QRPA ones; i.e., the theory takes into account all three known mechanisms of giant-resonance width. To the most extent, the theory was developed and applied to nuclei without pairing. A quantitative explanation of the giant-resonance widths was obtained, with the complex configurations contributing about half of the width. In addition, a large part of the observed giant-resonance gross and fine structures can be directly traced back to the specific complex configurations, and the recent results of the (α, α′) experiments in ⁴⁰Ca and ⁵⁸Ni could be explained. Consistent use of the Green’s function method makes it possible to include and calculate some effects which were practically unstudied earlier. These are ground-state correlations induced by complex configurations and “refined” basis effects, in particular, the second (or quasiparticle-phonon) mechanism of pairing. Both of them can be studied in current experiments. In the past five years, the ETFFS has been developed and applied actively to even—even and odd-mass nuclei with pairing. Calculations of the E1 pygmy resonance in Ca and Sn isotopes have shown that this phenomenon, which is important for (n, γ) and (γ, n) reactions, cannot be explained without allowing for complex configurations. Consideration of the single-particle continuum and the practical universality of the interaction parameters allow the ETFFS to be used for calculations of unstable nuclei. The prospects and status of the necessary development of a self-consistent ETFFS for nuclei with pairing are discussed. The text was submitted by the author in English.     

Conductance Distribution in 1D Systems: Dependence on the Fermi Level and the Ideal Leads

Journal of Experimental and Theoretical Physics - The correct definition of the conductance of finite systems implies a connection to the system of the massive ideal leads. Influence of the latter...     

Energy Fluctuation of Ideal Fermi Gas Trapped under Generic Power Law Potential U=Σ_(i=1)~d c_i|x_i/a_i|~(n_i) in d Dimensions

Energy fluctuation of ideal Fermi gas trapped under generic power law potential U=Σ_(i=1)~d c_i|x_i/a_i|~(n_i) has been calculated in arbitrary dimensions.Energy fluctuation is scrutinized further in the degenerate limit μK_B T with the help of Sommerfeld expansion.The dependence of energy fluctuation on dimensionality and power law potential is studied in detail.Most importantly our general result can not only exactly reproduce the recently published result regarding free and harmonically trapped ideal Fermi gas in d =3 but also can describe the outcome for any power law potential in arbitrary dimension.     

Large Detuning Limit for the Multipartite Systems Interacting with Electromagnetic Fields

We study the dynamics of the multipartite systems nonresonantly interacting with electromagnetic fields, focusing on the large detuning limit for the effective Hamiltonian. Due to the many-particle interference effects, the more rigorous large detuning condition for neglecting the rapidly oscillating terms for the effective Hamiltonian should be N 1/2 g, instead of g usually used in the literature even in the case of multipartite systems, with N the number of microparticles involved, g the coupling strength, the detuning. This result is significant since merely the satisfaction of the original condition will result in the invalidity of the effective Hamiltonian and the errors of the parameters associated with the detuning in the multipartite case.