Non-Markovianity in the presence of multiple thermal environments via collision model

By means of the collision model, we study the non-Markovianity of an open quantum system S being coupled to M thermal reservoirs. In our model, each reservoir is modeled as a chain of ancillas whose intracollisions account for the occurrence of non-Markovian dynamics. We show that by incorporating M reservoir ancillas into the system, the non-Markovian dynamics of S can be embedded in the extended system that experiences a completely Markovian dynamics. The number M of involved reservoirs can thus be identified as the memory depth and determines the degree of the non-Markovianity. In the equilibrium case with identical temperatures for all the reservoirs, we show that though the non-Markovianity is proportional to M in the zero and relatively low temperature regimes, in the relatively high temperature regime such proportional relation holds only for the weak intracollisions of the reservoir ancillas. In the nonequilibrium situation, we examine the effect of temperature difference of reservoirs on the non-Markovianity. Focusing on a simple situation with two reservoirs, we observe that the nonzero temperature difference has a significant impact on the non-Markovianity.     

The discrete Gaussian chain with 1/r n interactions: Exact results

We show that the discrete Gaussian chain with interactionV(r) = 1/(r ²–1/4) is self-dual. At the dual temperaturek _B T = 1 we calculate the height-height correlation function and find that the system is rough. A duality relation is established for the temperature-dependent correlation function exponent. We also consider interactionsV(r)–1/r ⁿ and show that absence of a phase transition for 2 <n < 3 implies absence of a phase transition for 1 <n < 2. All these results have their counterparts in a linear system of charges interacting through a potential which is asymptotically logarithmic (forn = 2) or power-law-like (forn 2.On leave of absence from Chemistry Laboratory III, Universitetsparken 5, 2100 ©, Copenhagen, Denmark.     

Exact solution of the Gaudin model with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions

We study the exact solution of the Gaudin model with Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions. The energy and Bethe ansatz equations of the Gaudin model can be obtained via the off-diagonal Bethe ansatz method. Based on the off-diagonal Bethe ansatz solutions, we construct the Bethe states of the inhomogeneous X X X Heisenberg spin chain with the generic open boundaries. By taking a quasi-classical limit, we give explicit closed-form expression of the Bethe states of the Gaudin model. From the numerical simulations for the small-size system, it is shown that some Bethe roots go to infinity when the Gaudin model recovers the U(1) symmetry. Furthermore,it is found that the contribution of those Bethe roots to the Bethe states is a nonzero constant. This fact enables us to recover the Bethe states of the Gaudin model with the U(1) symmetry. These results provide a basis for the further study of the thermodynamic limit, correlation functions, and quantum dynamics of the Gaudin model.     

Quantum spherical model with competing interactions

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T$T$, a quantum parameter g$g$, and the ratio p=−_J2/_J1$p=-J_2/J_1$, where _J1>0$J_1>0$ refers to ferromagnetic interactions between first-neighbour sites along the d$d$ directions of a hypercubic lattice, and _J2<0$J_2<0$ is associated with competing antiferromagnetic interactions between second neighbours along m≤d$m\le d$ directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g=0$g=0$ space, with a Lifshitz point at p=1/4$p=1/4$, for d>2$d>2$, and closed-form expressions for the decay of the pair correlations in one dimension. In the T=0$T=0$ phase diagram, there is a critical border, _gc=_gc(p)$g_c=g_c\left(p\right)$ for d≥2$d\ge 2$, with a singularity at the Lifshitz point if d<(m+4)/2$d<(m+4)/2$. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p=1/4$p=1/4$.     

二能级原子与逆场算符耦合系统的J-C模型

利用表象变换方法,对含逆场算符的J-C模型,分别在相互作用表象中和薛定谔表象中求出了系统的演化波函数,并讨论了失谐量为零时的拉比振动.     

order and disorder lines in systems with competing interactions: II. The IRF model

Systems with competing interactions can be often exactly solved on a restricted subspace of the parameter space, called an order or disorder trajectory. A simple method introduced within the transfer matrix formalism allows for the calculation of the free energy and spin-spin correlation functions along the order and disorder lines of the Ising model with all possible interactions around a face of the square lattice (IRF model). The general eight-vertex model is thoroughly examined and shows full analogy with the quantum spin chain results of the previous paper.On leave from and address after September 1, 1982: Institute for Theoretical Physics, Eötvös University, 1088 Budapest, Puskin U. 5–7, Hungary.     

The one-dimensional 1/4-filled Hubbard model with alternating interactions

The one-dimensional Hubbard model with different on-site interaction on the even (U_a) and odd (U_b) sites is considered within the framework of the weak coupling approach. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system and to the dynamical generation of a commensurability gap in the charge excitation spectrum for U_a ≠ U_b and U_a>0 or U_b>0. Depending on the relation between the bare coupling constants the system shows four different regimes of behaviour in the infrared limit corresponding to normal metal, nonmagnetic insulator, antiferromagnetic insulator and superconducting states. The extended model including interaction between particles on nearest and next-nearest neighbour sites is also considered.     

Method for construction of operators in Fock space

It is shown, by providing a general method for the construction that any Fock space linear operator defined on the dense linear manifold spanned by the particle number representation basis can be represented in terms of the annihilation and creation operators. The normal form of the representation is unique.     

Spectral properties of Kirkwood-Salsburg and Kirkwood-Ruelle operators

A method for solving Kirkwood-type equations in Banach spacesE () andE ^S () is applied to derive spectral properties of Kirkwood-Salsburg and Kirkwood-Ruelle operators in these spaces. For stable interactions these operators are shown to have, besides the point spectrum, a residual one. We establish also that the residual spectrum may disappear if a superstable (singular) interaction between particles is switched on. In this case the bounded Kirkwood-Salsburg operator is proved to have a zero Fredholm radius.     

Microscopic model for superexchange interactions and photomagnetism in binuclear transition metal complexes

Recent experiments show that the superexchange interaction in molecular clusters containing transition metal ions A?=?Ni^II and B?=?W^V, Nb^IV or Mo^V in some cases is antiferromagnetic, contrary to the conventional superexchange rules. To understand this anomaly, we develop a quantum many-body model Hamiltonian and solve it exactly using a valence bond (VB) approach. We identify the various model parameters which control the ground state spin in different clusters of the A-B system. We present quantum phase diagrams that delineate the high and low-spin ground states in the parameter space. We fit the spin gap to a spin Hamiltonian and extract the effective exchange constant within the experimentally observed range, for reasonable parameter values. We also find a region of intermediate spin ground state in the parameter space, in clusters of larger size. The spin spectrum of the microscopic model cannot be reproduced by a simple Heisenberg exchange Hamiltonian. The above microscopic model is generic and can also be employed to explain photomagnetism in the MoCu₆ system. We solve the model for MoCu₆ and find that ground state is degenerate and is spanned by the S?=?0,?1,?2 and 3 manifolds with doubly occupied Mo site corresponding to Mo(IV) and singly occupied Cu sites corresponding to Cu(II) configurations. In each of these spin spaces, we observe that there exist charge-transfer (CT) states at ≈3?eV above the ground state which are dipole coupled to the ground state. The transition dipole in the S?=?3 manifold is the largest for the CT excitations. Coupled with the fact that the density of states of the S?=?3 manifold is sparse, compared to other spin manifolds, we expect that the S?=?3 CT excited state to be long-lived, thereby explaining the experimentally observed photomagnetism in the MoCu₆ system.     

Phonon thermal transport in InAs nanowires with different size and growth directions

We investigate the phonon thermal transport properties in InAs nanowires with different size and growth directions by using nonequilibrium molecular dynamics methods. The results show a remarkable anisotropy for the thermal conductivity in InAs nanowire. It is found that the thermal conductivity along [110] growth direction is about three times larger than that along [100] or [111] direction. With the increase of temperature, the thermal conductivity along [110] direction decreases significantly. However, the thermal conductivity along other two directions is not sensitive to temperature. Moreover, we find a crossover from ballistic to ballistic-diffusive thermal transport for a certain length of InAs nanowire. A brief physical analysis of these results is given. It is suggested that the anisotropy of thermal conductivity is common for nanowires with zinc blende structures.     

Effective operators and the truncation of shell model configuration space

An alternative derivation of the projection method for constructing effective operators in the truncated shell model space is presented. The results of explicit numerical calculations in three different nuclear regions are discussed. Non-hermiticity of the effective Hamiltonian and various hermitisation procedures are investigated in detail.     

Exact solution for the thermo Jaynes--Cummings model

Based on the construction of supersymmetric generators, we use the Lewis--Riesenfeld invariant method to deduce the exact and explicit eigen-energy spectrum with the time-dependent thermo Jaynes--Cummings model. One of the advantages of this approach is that it can transform the hidden form, related to the chronological product, of the time evolution operator into an explicit expression. Moreover, the dynamical and statistics properties of physical quantities are obtained for the given initial states in the thermo Jaynes--Cummings system.     

Landau系统四类规范不变的升降算符

借助圆心坐标算符和初机械动量算符,给出Landau系统(带电粒子在垂直于均匀磁场平面内的运动)的四类升降算符,并讨论相应的选择定则和守恒量子数 关键词： Landau系统 升降算符     

Motion and capture in the presence of cooperative trap interactions II: Exact calculations for perfect absorbers in one dimension

Exact calculations are presented for the survival fraction and other capturerelated observables in a problem involving migration on a one-dimensional lattice containing perfectly absorbing traps whose placement within the crystal is determined by explicit interactions among the trap molecules. These interactions, which are treated exactly in a lattice-gas model, may be attractive, in which case they lead to trap cluster formation and a reduction of the trapping efficiency, or they may be repulsive thus leading to increased separation of the trap molecules and an enhancement of the trapping process.Supported in part by the National Science Foundation under Grant Nos. DMR-8111434 and INT-8210098.     

Exact results for a dilute Potts model

Exact results are obtained for the annealed, dilute,q-component Potts model on the decorated square lattice. The phase diagram is found to consist of a high-temperature region, a low-temperature region, and a two-phase region in between which arises only forq>4: exact expressions for the phase boundary and the critical probability are derived. At the critical point the specific heat is generally finite and has a cusp; the slope of the cusp is finite forq=4 and infinite (vertical) forq=2 and 3.Work supported in part by NSF Grant No. DMR 78-18808.