Two interacting particles in a random potential: mapping onto one parameter localization theories without interaction

We consider two models for a pair of interacting particles in a random potential: (i) two particles with a Hubbard interaction in arbitrary dimensions and (ii) a strongly bound pair in one dimension. Establishing suitable correspondences we demonstrate that both cases can be described in terms familiar from theories of non-interacting particles. In particular, these two cases are shown to be controlled by a single scaling variable, namely the pair conductance g ₂. For an attractive or repulsive Hubbard interaction and starting from a certain effective Hamiltonian we derive a supersymmetric nonlinear σ model. Its action turns out to be closely related to the one found by Efetov for noninteracting electrons in disordered metals. This enables us to describe the diffusive motion of the particle pair on scales exceeding the oneparticle localization length L ₁ and to discuss the corresponding level statistics. For tightly bound pairs in one dimension, on the other hand, we follow early work by Dorokhov and exploit the analogy with the transfer matrix approach to quasi-1d conductors. Extending our study to M particles we obtain a M-particle localization length scaling like the Mth power of the one-particle localization length.     

Interaction induced delocalization of two particles: large system size calculations and dependence on interaction strength

The localization length L₂ of two interacting particles in a one-dimensional disordered system is studied for very large system sizes by an efficient and accurate variant of the Green function method. The numerical results (at the band center) can be well described by the functional form L ₂ =L ₁ [0.5+c(U) L ₁ ] where L₁ is the one-particle localization length and the coefficient depends on the strength U of the on-site Hubbard interaction. The Breit-Wigner width or equivalently the (inverse) life time of non-interacting pair states is analytically calculated for small disorder and taking into account the energy dependence of the one-particle localization length. This provides a consistent theoretical explanation of the numerically found U-dependence of c(U). Received 16 September 1998     

A single parameter scaling theory in a disordered layered system

We show that in a disordered layered system all states are localized if k_Fl<4Πg_c, irrespective of the interlayer coupling t _⊥. The crossover of dimensionality depends on t_⊥. Near the critical value t_⊥^c at which the Anderson transition occurs, the correlation length ζ^m and the localization length ζ^loc are calculated.     

Quantum diffusion and scaling of localized interacting electrons

A new numerical method is introduced that enables a reliable study of disorder‐induced localization of interacting particles. It is based on a quantum mechanical time evolution calculation combined with a finite size scaling analysis. The time evolution of up to four particles in one dimension is studied and localization lengths are defined via the long‐time saturation values of the mean radius, the inverse participation ratio and the center of mass extension. A systematic study of finite size effects using the finite size scaling method is performed in order to extract the localization lengths in the limit of an infinite system size. For a single particle, the well‐known scaling of the localization length λ₁ with disorder strength W is observed, λ₁ ∝ W^—2. For two particles, an interaction‐induced delocalization is found, confirming previous results obtained by numerically calculating matrix elements of the two‐particle Green's function: in the limit of small disorder, the localization length increases with decreasing disorder as λ₂ ∝ W^—4 and can be much larger than <$>\mitlambda λ₁. For three and four particles, delocalization is even stronger. Based on analytical arguments, an upper bound for the n‐particle localization length λ_n is derived and shown to be in agreement with the numerical data, λ_n ∝ λ₁. Although the localization length increases superexponentially with particle number and can become arbitrarily large for small disorder, it does not diverge for finite λ₁ and n. Hence, no extendedstates exist in one dimension, at least for spinless fermions.     

Amplification in one-dimensional random active medium near the lasing threshold

We studied the transmittance of a random amplifying medium near the lasing threshold by using the convergence criterion proposed by Nam and Zhang [Phys. Rev. B 66 73101, 2002] that allows separating the physical solutions of the time-independent Maxwell equations from the unphysical ones and describing critical size L _c of a random system in statistical terms. We found that the dependence of the critical gain ∈ ^″ _c (at which the lasing threshold occurs) as a function of number of layers is configuration-dependent and thus the lasing condition for random media is described by means of the probability of finding of physical solutions and evaluated by averaging over the ensemble of random configurations. By employing this approach we inspect the validity of the two-parameter scaling model by Zhang [Phys. Rev. B 52 7960, 1995], according to which the behavior of the random system with gain is described by relation 1/ξ = 1/ξ ₀ + 1/l _g, where ξ and ξ ₀ are localization length with and without gain, respectively, and l _g = 2/ω∈ ^″, is gain length, where ∈ ^″ is imaginary part of the dielectric constant that represents gain. We show that the range of validity of this relation depends on the ratio of both lengths and also affects the slope of the ln Λ_c(q) (where Λ_c ≡ L _c/ξ ₀ is normalized critical size and q ^?1 ≡ l _g/ξ ₀ is dimensionless gain length). We extend the study of the relation for the critical size L _c by inspecting the dependence of the slope of the ln Λ_c(q) on the strength of the randomness. We interpret its behavior in terms of the statistical properties of the localized states. Namely, by studying of the variance of the Lyapunov exponent λ (the inverse of the localization length ξ ₀) we have found that the slope of the ln Λ_c(q)) reflects the transition between two different regimes of localization with Anderson and Lifshits-like behavior that is known to be indicated by peak in var(λ). We discuss the generalization of two-parameter scaling model by implementing revisited single parameter scaling (SPS) theory by Deych et al. [Phys. Rev. Lett. 84 2678, 2000] which allows describing non-SPS regime in terms of a new scale l _s.

     

Transverse spin correlations in a random anisotropy system: Amorphous ErCo2

We provide a coherent interpretation of early small angle scattering experiments performed by some of us on amorphous ErCo₂ [9]. At low temperature the zero field transverse spin-spin correlation function is found to fit a simple exponential for large length scales (l >l_c), supporting the lower critical dimensionality d_c=4. For shorter length scales (l<l_c) the correlation function is of the Ornstein-Zernike type. These results are physically understood in terms of the breaking of ferromagnetism into Imry and Ma domains.A further physical interpretation leads us to consider the localization of ferromagnetic spin waves within Imry and Ma domains in zero field, and their delocalization by application of an external field.     

Nonlinear quantum theory of interaction of charged particles and monochromatic radiation in a medium

We study the quantum theory of nonlinear interaction of charged particles and a given field of plane-transverse electromagnetic radiation in a medium. Using the exact solution of the generalized Lamé equation, we find the nonlinear solution of the Mathieu equation to which the relativistic quantum equation of particle motion in the field of a monochromatic wave in the medium reduces if one ignores the spin-spin interaction (the Klein-Gordon equation).We study the stability of solutions of the generalized Lamé equation and find a class of bounded solutions corresponding to the wave function of the particle. On the basis of this solution we establish that the particle states in a stimulated Cherenkov process form bands. Depending on the wave intensity and polarization, such a band structure describes both bound particle-wave states (capture) and states in the continuous spectrum. It is obvious that in a plasma there can be no such bands, since bound states of a particle with a transverse wave whose phase velocity v _ph is higher than c are impossible in this case. The method developed in the paper can be applied to a broad class of problems reducible to the solution of the Mathieu equation. Zh. éksp. Teor. Fiz. 113, 43–57 (January 1998)     

Two interacting particles in a disordered chain I: Multifractality of the interaction matrix elements

For N interacting particles in a one dimensional random potential, we study the structure of the corresponding network in Hilbert space. The states without interaction play the role of the “sites”. The hopping terms are induced by the interaction. When the one body states are localized, we numerically find that the set of directly connected “sites” is multifractal. For the case of two interacting particles, the fractal dimension associated to the second moment of the hopping term is shown to characterize the Golden rule decay of the non interacting states and the enhancement factor of the localization length. Received: 17 April 1998 / Accepted: 14 May 1998     

Potentials of pointlike particles in gauge theory with a dilaton

I examine the potential of a pointlike particle carrying SU (N _c) charge in a gauge theory with a dilaton. The potential depends on boundary conditions imposed on the dilaton: For a dilaton that vanishes at infinity the resulting potential is a regulatized Coulomb potential of the form (r+r _ϕ)⁻¹, withr _ϕ, inversely proportional to the decay constant of the dilaton. Another natural constraint on the dialaton ϕ is independence of (1/g ²) exp(ϕ/f_ϕ) from the gauge couplingg. This requirement yields a confining potential proportional tor.     

基于幂次相互作用的二维磁性团簇耦合能研究

在扩散限制凝聚模型基础上,采用Monte Carlo方法模拟了磁耦合作用随粒子间距离幂次变化的磁性粒子动力学凝聚过程.重点研究了在不同幂指数α值下团簇在生长过程中,即随着粒子数N的增加,团簇平均耦合能E_c(N)的演化过程.模拟结果表明:对于α≥5时,E_c(N)随着粒子数N的增加变化较小;当α=2时,E关键词： 扩散限制凝聚模型 幂次相互作用 耦合能     

Two interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states

For two particles in a disordered chain of length L with on-site interaction U, a duality transformation maps the behavior at weak interaction onto the behavior at strong interaction. Around the fixed point of this transformation, the interaction yields a maximum mixing of the one body states. When (the one particle localization length), this mixing results in weak chaos accompanied by multifractal wave functions and critical spectral statistics, as in the one particle problem at the mobility edge or in certain pseudo-integrable billiards. In one dimension, a local interaction can only yield this weak chaos but can never drive the two particle system to full chaos with Wigner-Dyson statistics. Received: 22 May 1998 / Received in final form: 24 August 1998 / Accepted: 4 September 1998     

Charmed Deuteron

Possible existence of bound states of a charmed baryon, Λ _c , Σ _c , Σ* _c with a nucleon, N, as well as two charmed baryons, Λ _c Λ _c , etc., are examined in the meson exchange potential approach. The heavy quark spin symmetry induces a strong tensor coupling between Λ _c N, Σ _c N and Σ* _c N states, which causes a bound state of Λ _c N (J = 0⁺ and 1⁺) states. Such a bound state is also seen in the spin-singlet Λ _c Λ _c channel, which resembles the H dibaryon in the strange sector.     

Vibration-rotation bands of nitrous oxide: 4.1 micron region

The infrared spectrum of nitrous oxide has been measured and analyzed from 2265 cm^?1 to 2615 cm^?1. Newly refined effective rotational constants for twenty-one vibrational states of ¹⁴N₂O, three vibrational states each of ¹⁴N₂¹⁸O and ¹⁵N¹⁴N¹⁶O, two states of ¹⁴N¹⁵N¹⁶O and one state of ¹⁴N₂¹⁷O have been calculated.The most interesting features observed are two Δ-Σ “forbidden” bands, 04^2c0-00⁰0 and 12^2c0-00⁰0. These bands occur because of Coriolis interaction between unperturbed vibrational states having l = 0 and l = 2.     

Existence of enantiomeric phase separation in a three-dimensional lattice gas model

A three-dimensional lattice gas model for enantiomeric phase separation is introduced. The enantiomeric molecules (d andl) are the two nonsuperimposable mirror images having the molecular structure C(AB)₂, where C is a tetrahedrally bonded carbon atom with one bond to each end of two AB groups. The lattice gas model consists of a body-centered cubic lattice, each site of which can be either vacant or occupied by a molecule oriented so that the A and B groups point toward neighboring lattice sites. Pairs of molecules interact with short-range, orientationally-dependent interactions. For a domain of interaction parameters, the Pirogov-Sinai extension of the Peierls argument is used to prove thatd-rich andl-rich phases exist in the model at sufficiently low temperature. For another domain of interaction parameters, at sufficiently high chemical potential there is an infinite number of ground states, each containing a racemic mixture ofd andl molecules.     

Rotation of a self-bound many-body system

We discuss the rotational excitations of highly quantum many-body systems (for example, polyatomic molecules or microdroplets of helium). For a general system, the states F?, where and ? is a rotationally invariant ground or vibrational state, are shown to be eigenfunctions of L ² and L_z , with eigenvalues L(L+1)? ² and L? (for even L). These wavefunctions preserve the translational invariance and the permutation and inversion symmetries of the N-particle state ?. For harmonic pair interactions, the f = 1 wavefunctions are shown to be exact eigenstates of the N-body hamiltonian. For large N, the states F?(f=1) represent surface oscillations of the type first proposed by Bohr. An inequality for the rotational excitation energy is obtained variationally; it depends on two, three, and four-particle correlations. Other translationally invariant angular momentum eigenfunctions are also discussed.     

Electronic properties of one-dimensional systems with long-range correlated binary potentials

We study numerically the electronic properties of one-dimensional systems with long-range correlated binary potentials.The potentials are mapped from binary sequences with a power-law power spectrum over the entire frequency range,which is characterized by correlation exponent β.We find the localization length ξ increases with β.At system sizes N →∞,there are no extended states.However,there exists a transition at a threshold β c.When β > β c,we obtain ξ > 0.On the other hand,at finite system sizes,ξ≥ N may happen at certain β,which makes the system "metallic",and the upper-bound system size N (β) is given.     

Quantum-gas model estimate for wide range of superconducting critical temperatures

A quantum mechanical model requiring only strong quantum interaction for a charged particle gas estimates the superconducting transition temperature for wide-ranging states of matter. A general equation is derived which estimates the critical temperatureT _c the energy gap, and the coherence length for the classical metallic superconductors, heavy-electron superconductors, the perovskites, metallic hydrogen, and neutron stars. Estimates forT _c , the coherence length, and the energy gap which are model independent for coupling mechanisms agree well with accepted values for these materials. Estimates are made for threedimensional quasi-two and quasi-one-dimensional states.     

Tc of superconducting alloys with narrow energy bands

The vertex equation for a Cooper pair is solved for T_c of an A—B alloy, assuming a single-site interaction between electrons. The result depends on the partial densities of state N_A(O), N_B(O), the intra-atomic Coulomb repulsions, and the attractive interaction which contains the normal-mode density g(z) and the matrix elements of the ion-potential gradients between two electrons at one and the same site.