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1.
It is shown that certain ensembles of random matrices with entries that vanish outside a band around the diagonal satisfy
a localization condition on the resolvent which guarantees that eigenvectors have strong overlap with a vanishing fraction
of standard basis vectors, provided the band width W raised to a power μ remains smaller than the matrix size N. For a Gaussian band ensemble, with matrix elements given by i.i.d. centered Gaussians within a band of width W, the estimate μ ≤ 8 holds. 相似文献
2.
We investigate the influence of the Coulomb interaction on the energy spectrum of a finite number of electrons in a geometrically confined quantum mechanical system. The spectrum is calculated numerically using the Slater determinants of the one-electron states as basis set. It is found to be dominated by the Coulomb repulsion when the system is large. Coulomb and exchange matrix elements for a given combination of four one-electron states are of the same order of magnitude. As a consequence, the energy difference between the ground states of the ( N+1)- and the N-electron system is an order of magnitude smaller than each of the matrix elements, although being much larger than the separation of the one-electron energy levels. We discuss the importance of the interaction effects for the explanation of the recently observed resonant behavior of the electronic transport through quantum dots. 相似文献
3.
We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary N × N matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite qudit systems. The structure of the maps is inspired by “portrait” map of the probability vectors corresponding to the action on the vectors by stochastic matrices containing either unity or zero matrix elements. We obtain new entropic inequalities for arbitrary qudit states including a single qudit and discuss entangled single qudit state. We consider in detail the examples of N = 3 and 4. Also we point out the possible use of entangled states of systems without subsystems (e.g., a single qudit) as a resource for quantum computations. 相似文献
4.
A transfer-matrix for the multichannel scattering problem is obtained. The elements of this matrix are expressed in terms
of transmission and reflection amplitudes. On the basis of the matrix for a system of N localized and nonoverlapped scattering centers the recurrent equations for the transfermatrix elements are derived and the
initial conditions are defined. 相似文献
5.
We introduce a suitable adapted ordering for the twisted N= 2 superconformal algebra (i.e. with mixed boundary conditions for the fermionic fields). We show that the ordering kernels
for complete Verma modules have two elements and the ordering kernels for G-closed Verma modules just one. Therefore, spaces of singular vectors may be two-dimensional for complete Verma modules whilst
for G-closed Verma modules they can only be one-dimensional. We give all singular vectors for the levels , 1, and for both complete Verma modules and G-closed Verma modules. We also give explicit
examples of degenerate cases with two-dimensional singular vector spaces in complete Verma modules. General expressions are
conjectured for the relevant terms of all (primitive) singular vectors, i.e. for the coefficients with respect to the ordering
kernel. These expressions allow to identify all degenerate cases as well as all G-closed singular vectors. They also lead to the discovery of subsingular vectors for the twisted N= 2 superconformal algebra. Explicit examples of these subsingular vectors are given for the levels , 1, and . Finally, the multiplication rules for singular vector operators are derived using the ordering kernel coefficients. This
sets the basis for the analysis of the twisted N= 2 embedding diagrams.
Received: Received: 15 March 1999 / Accepted: 12 November 2000 相似文献
6.
A Coulomb-modified matrix of scattering amplitudes (an [( F)\tilde]\tilde F matrix) is considered for the case of two coupled channels of elastic scattering of charged particles with different orbital
angular momenta ( l
1 and l
2 = l
1 + 2). Matrix elements of the [( F)\tilde]\tilde F matrix are expressed in terms of the matrix elements of a [( K)\tilde] - 1\tilde K^{ - 1} matrix inverse to a modified reaction K matrix. The elements of the [( K)\tilde] - 1\tilde K^{ - 1} matrix are written as expansions that are generalizations of single-channel effective range expansion with allowance for
the Coulomb interaction. If a system of colliding particles involves a bound state, the analytic continuation of these expansions
into the region of negative energies makes it possible to obtain both the position of the pole corresponding to the bound
state and the scattering amplitude residues in this pole, in terms of which the corresponding vertex constants and asymptotic
normalization coefficients are expressed. 相似文献
7.
We employ Monte Carlo simulations to numerically study the temporal evolution and transient oscillations of the population
densities, the associated frequency power spectra, and the spatial correlation functions in the (quasi-) steady state in two-dimensional
stochastic May-Leonard models
of mobile individuals, allowing for particle exchanges with nearest-neighbors and hopping onto empty sites.
We therefore consider a class of four-state three-species cyclic predator-prey models whose total particle number is not conserved.
We demonstrate that quenched disorder in either the reaction or in the mobility
rates hardly impacts the dynamical evolution, the emergence and structure of spiral patterns, or the mean extinction time
in this system. We also show that direct particle pair exchange processes promote the formation of regular spiral structures.
Moreover, upon increasing the rates of mobility, we observe a remarkable change in the extinction properties in the May-Leonard
system (for small system sizes):
(1) as the mobility rate exceeds a threshold that separates a species coexistence (quasi-) steady state from an absorbing
state, the mean extinction time as function of system size N crosses over from a functional form ∼ e
cN
/ N (where c is a constant) to a linear dependence; (2) the measured histogram of extinction times displays a corresponding crossover
from an (approximately) exponential to a Gaussian distribution. The latter results are found to hold true also when the mobility
rates are randomly distributed. 相似文献
8.
We derive spin operator matrix elements between general eigenstates of the superintegrable ℤ
N
-symmetric chiral Potts quantum chain of finite length. Our starting point is the extended Onsager algebra recently proposed
by Baxter. For each pair of spaces (Onsager sectors) of the irreducible representations of the Onsager algebra, we calculate
the spin matrix elements between the eigenstates of the Hamiltonian of the quantum chain in factorized form, up to an overall
scalar factor. This factor is known for the ground state Onsager sectors. For the matrix elements between the ground states
of these sectors we perform the thermodynamic limit and obtain the formula for the order parameters. For the Ising quantum
chain in a transverse field ( N=2 case) the factorized form for the matrix elements coincides with the corresponding expressions obtained recently by the
Separation of Variables method. 相似文献
9.
The quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite
quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications
in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes,
and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our
result can be viewed as an analogue of the Sing-Thompson Theorem (respectively Horn’s Lemma), characterizing the relationship
between main diagonal elements and singular values of a complex matrix: We find necessary and sufficient conditions for vectors
( d
1,..., d
n
) and ( c
1,..., c
n
) to be the symplectic eigenvalues and symplectic main diagonal elements of a strictly positive real matrix, respectively.
More physically speaking, this result determines what local temperatures or entropies are consistent with a pure or mixed
Gaussian state of several modes. We find that this result implies a solution to the problem of sharing of entanglement in
pure Gaussian states and allows for estimating the global entropy of non-Gaussian states based on local measurements. Implications
to the actual preparation of multi-mode continuous-variable entangled states are discussed. We compare the findings with the
marginal problem for qubits, the solution of which for pure states has a strikingly similar and in fact simple form. 相似文献
10.
In this paper, both fast Fourier transformation (FFT) and preconditioned CG technique are introduced into method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. Electromagnetic wave scattering by an infinite plane metallic grating is used as the examples to describe its implementation. For arbitrary incident wave, Helmholz equation and boundary condition are first transformed into new ones so that the impedance matrix elements are calculated by FFT technique. As a result, this Topelitz impedance matrix only requires O( N) memory storage for the conjugate gradient FFT method to solve the current distribution with the computational complexity O( N log N) . Our numerical results show that circulate matrix preconditioner can speed up CG-FFT method to converge in much smaller CPU time than the banded matrix preconditioner. 相似文献
11.
We study a nonrelativistic quantum system coupled, via a quadratic interaction [cf. formula (1.10) below], to a free Boson gas in the Fock state. We prove that, in the low density limit ( z
2=fugacity0), the matrix elements of the wave operator of the system at time t/z
2 in the collective coherent vectors converge to the matrix elements, in suitable coherent vectors of the quantum Brownian motion process, of a unitary Markovian cocycle satisfying a quantum stochastic differential equation driven by some pure number process (i.e. no quantum diffusion part and only the quantum analogue of the purely discontinuous, or jump, processes). This proves that the number (or quantum Poisson) processes, introduced by Hudson and Parthasarathy and studied by Frigerio and Maassen, arise effectively as conjectured by the latter two authors as low density limits of Hamiltonian models. 相似文献
12.
We consider the evolution of a system composed of N non-interacting point particles of mass m in a cylindrical container divided into two regions by a movable adiabatic wall (the adiabatic piston). We study the thermodynamic limit for the piston where the area A of the cross-section, the mass M of the piston, and the number N of particles go to infinity keeping A/ M and N/ M fixed. The length of the container is a fixed parameter which can be either finite or infinite. In this thermodynamic limit we show that the motion of the piston is deterministic and the evolution is adiabatic. Moreover if the length of the container is infinite, we show that the piston evolves toward a stationary state with velocity approximately proportional to the pressure difference. If the length of the container is finite, introducing a simplifying assumption we show that the system evolves with either weak or strong damping toward a well-defined state of mechanical equilibrium where the pressures are the same, but the temperatures different. Numerical simulations are presented to illustrate possible evolutions and to check the validity of the assumption. 相似文献
13.
The effective matrix elements which appear in pre-equilibrium calculations in the rate expressions for the residual two-body interactions have been evaluated from analyses of emitted particle energy spectra. Probably because of details in the model formulation, the results are found to depend on the nature of the projectile. They are, however, of reasonable magnitude and show a mass number and excitation energy dependence consistent with predictions based on calculations of mean free paths in nuclear matter. The square of the empirical effective matrix element is found to approximately obey the relation M2 = KaA−3E−1 with the values of Ka = 95 MeV 3 and 725 MeV 3 applying to proton and α-particle induced reactions respectively. The quantities A and E are the mass number and excitation energy of the system respectively. 相似文献
14.
In this second paper, using N = 3 polarized electrons (spinless fermions) interacting via a U/ r Coulomb repulsion on a two dimensional L× L square lattice with periodic boundary conditions and nearest neighbor hopping t, we show that a single unpaired fermion can co-exist with a correlated two particle Wigner molecule for intermediate values
of the Coulomb energy to kinetic energy ratio r
s = UL/(2 t
). This supports in an ultimate mesoscopic limit a possibility proposed by Andreev and Lifshitz for the thermodynamic limit:
a quantum crystal may have delocalized defects without melting, the number of sites of the crystalline array being smaller
than the total number of particles. When L = 6, the ground state exhibits four regimes as r s increases: a Hartree-Fock regime, a first supersolid regime where a correlated pair co-exists with a third fully delocalized
particle, a second supersolid regime where the third particle is partly delocalized, and eventually a correlated lattice regime.
Received 22 October 2002 Published online 23 May 2003
RID="a"
ID="a"e-mail: jpichard@cea.fr 相似文献
15.
In this paper we consider the dynamics of harmonically-confined atomic gases. We present various general results which are independent of particle statistics, interatomic interactions and dimensionality. Of particular interest is the response of the system to external perturbations which can be either static or dynamic in nature. We prove an extended Harmonic Potential Theorem which is useful in determining the damping of the centre of mass motion when the system is prepared initially in a highly nonequilibrium state. We also study the response of the gas to a dynamic external potential whose position is made to oscillate sinusoidally in a given direction. We show in this case that either the energy absorption rate or the centre of mass dynamics can serve as a probe of the optical conductivity of the system. 相似文献
16.
We present a new independent scheme of SO(3) group transformations suitable for the N particle system, composed of N − 1 and 1 particle subsystems, where N − 1 particles have their own intrinsic clusterization. The simple expressions for corresponding four-particle harmonic-oscillator
transformation brackets are presented, as well as their simplifications for the special values of mass ratio parameters d = 0, d → ∞ and d
1 = 0, d
1 → ∞. 相似文献
17.
The nonmesonic decay of Λ-hypernuclei provides access to the nonleptonic weak decay process Λ N → NN, which is achievable only through the observation of hypernuclear ground-state decays. We continue the discussion of some
specific cases which make it possible to detect a few exclusive transitions, namely, the stripping of nucleon from the ground
state results in a resonance state decaying via emission of two clusters. Delayed clusters accompanying weak decay of light
hypernuclei give a unique information on spin dependence of the weak decay matrix elements. 相似文献
18.
The formation of the quark and lepton mass matrices through intermediate states of heavy mirror fermions is able to reproduce basic observable qualitative properties of weak-mixing matrices—specifically, the Cabibbo—Kobayashi—Maskawa (CKM) matrix and the Pontecorvo—Maki—Nakagawa-Sakata (PMNS) matrix. The reproduction in question includes the hierarchy of the CKM matrix elements and a general form of the PMNS matrix, including the smallness of the neutrino mixing angle θ13 and leads to extremely small neutrino masses. For leptons, these properties arise only if Standard Model neutrinos are Dirac particles and if the spectrum of their generations has an inverse character. In such a lepton system, the mechanism of spontaneous mirror-symmetry violation and the observed mass hierarchy of charged leptons (e, μ, and τ) specify the structure of the PMNS matrix and make it possible to estimate the complex-valuedness of its elements—that is, to assess the CP properties of leptons. In this case, the PMNS matrix does not involve Majorana phases, whereas its Dirac phase δCP corresponds to ∣ sin δCP ∣ that is substantially smaller than unity. 相似文献
19.
Rovibrational matrix elements of the multipole moments Q ? of HD, HT and DT for ranks 2 ≤ ? ≤ 11 have been computed. Since the present calculations have been performed with the nuclear centre of mass (rather than the geometric centre) as the origin, the computations had to include even as well as odd values of ?. The results are used to correlate the absorption intensities of the zero-phonon single transitions in solid HD to theory. 相似文献
20.
The S matrix and the scattering-amplitude matrix ( F matrix) are considered for the case of two coupled elastic-scattering channels differing by the values of the orbital angular
momentum ( l
1 and l
2 = l
1 + 2). The matrix elements of the S and F matrices in the absence of Coulomb interaction are expressed in terms of the matrix elements of the matrix K
−1 inverse to the reaction K matrix. The elements of the K
−1 matrix are written in the form of expansions that are generalizations of the single-channel effective-range expansion. If
there is a bound state in the system of colliding particles, then an analytic continuation of these expansions to the region
of negative energies makes it possible to obtain both the position of the pole corresponding to this bound state and the residues
of scattering amplitudes at this pole, the respective vertex constants and asymptotic normalization coefficients being expressed
in terms of these residues. By way of example, the developed formalism is applied to describing triplet neutron-proton scattering. 相似文献
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