共查询到20条相似文献,搜索用时 62 毫秒
1.
P. Littelmann H. -J. Sommers M. R. Zirnbauer 《Communications in Mathematical Physics》2008,283(2):343-395
‘Superbosonization’ is a new variant of the method of commuting and anti-commuting variables as used in studying random matrix
models of disordered and chaotic quantum systems. We here give a concise mathematical exposition of the key formulas of superbosonization.
Conceived by analogy with the bosonization technique for Dirac fermions, the new method differs from the traditional one in
that the superbosonization field is dual to the usual Hubbard-Stratonovich field. The present paper addresses invariant random
matrix ensembles with symmetry group U
n
, O
n
, or USp
n
, giving precise definitions and conditions of validity in each case. The method is illustrated at the example of Wegner’s
n-orbital model. Superbosonization promises to become a powerful tool for investigating the universality of spectral correlation
functions for a broad class of random matrix ensembles of non-Gaussian and/or non-invariant type. 相似文献
2.
This paper is devoted to the rigorous proof of the universality conjecture of random matrix theory, according to which the limiting eigenvalue statistics ofn×n random matrices within spectral intervals ofO(n
–1) is determined by the type of matrix (real symmetric, Hermitian, or quaternion real) and by the density of states. We prove this conjecture for a certain class of the Hermitian matrix ensembles that arise in the quantum field theory and have the unitary invariant distribution defined by a certain function (the potential in the quantum field theory) satisfying some regularity conditions. 相似文献
3.
Let λ
d
(p) be the p monomer-dimer entropy on the d-dimensional integer lattice ℤ
d
, where p∈[0,1] is the dimer density. We give upper and lower bounds for λ
d
(p) in terms of expressions involving λ
d−1(q). The upper bound is based on a conjecture claiming that the p monomer-dimer entropy of an infinite subset of ℤ
d
is bounded above by λ
d
(p). We compute the first three terms in the formal asymptotic expansion of λ
d
(p) in powers of
\frac1d\frac{1}{d}. We prove that the lower asymptotic matching conjecture is satisfied for λ
d
(p). Converted to a power series in p, our “formal” expansion shows remarkable validity in low dimensions, d=1,2,3, in which dimensions we give some numerical studies. 相似文献
4.
5.
Previous results on local asymptotic normality (LAN) for qubits [16, 19] are extended to quantum systems of arbitrary finite
dimension d. LAN means that the quantum statistical model consisting of n identically prepared d-dimensional systems with joint state converges as n → ∞ to a statistical model consisting of classical and quantum Gaussian variables with fixed and known covariance matrix,
and unknown means related to the parameters of the density matrix ρ. Remarkably, the limit model splits into a product of a classical Gaussian with mean equal to the diagonal parameters, and
independent harmonic oscillators prepared in thermal equilibrium states displaced by an amount proportional to the off-diagonal
elements. As in the qubits case [16], LAN is the main ingredient in devising a general two step adaptive procedure for the
optimal estimation of completely unknown d-dimensional quantum states. This measurement strategy shall be described in a forthcoming paper [18]. 相似文献
6.
采用三台可调谐激光实施孤立实激发,分三步将处于基态的Ba原子激发到6p1/2nd(J=1,3)和6p3/2nd(J=1,3)自电离态上,获得了分别从6snd1D2(n=7—15)和6snd3D2(n=7—12) 激发而得到的6p1/2nd(J=1,3)和6p3/2nd (J=1,3)自电离光谱,重点对主量子数n较低的自电离态进行了实验研究. 通过光谱的线形拟合得到了上述能级的位置和宽度等数据,进而获得了量子亏损和约化宽度等信息. 通过对不同系列的自电离光谱的分析和比较,详细讨论了这些自电离态的光谱特征及其复杂光谱结构的成因.
关键词:
孤立实激发
组态相互作用
自电离态 相似文献
7.
T. V. Dudnikova 《Russian Journal of Mathematical Physics》2006,13(2):123-130
We consider the dynamics of a harmonic crystal in n dimensions with d components, where d and n are arbitrary, d, n ⩾ 1. The initial data are given by a random function with finite mean energy density which also satisfies a Rosenblatt-or
Ibragimov-type mixing condition. The random function is close to diverse space-homogeneous processes as x
n
→ ±∞, with the distributions μ±. We prove that the phase flow is mixing with respect to the limit measure of statistical
solutions.
Partially supported by RFBR under grant no. 06-01-00096. 相似文献
8.
We stress that in contradiction with what happens in space dimensions n ≥ 3, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for a
large coupling constant. We give, in two dimensions, examples of weak potentials with one or infinitely many bound states.
We derive bounds for one and two dimensions which have the “right” coupling-constant behaviour for large coupling.
Received November 22, 2001; accepted for publication November 28, 2001 相似文献
9.
Converging lower bound to the critical screening parameterD
c
associated with the ground state of a two-particle system interacting through a cut-off Coulomb potential is obtained analytically
using an improved condition for the absence of bound states. The predicted numerical result for the lower bound is found to
be within 10−3% of the exact result. On the other hand, a multi-parameter variational approach yields a tight upper bound, within 0.54%
of the exact result. It is shown that the critical screening parameter for the exciteds-states can also be determined in an approximate way. We obtainD
c
ms
≈ [0.764435n
−2+0.617737n
−3]−1 wheren is the principal quantum number. The predictedD
c
for various quantum states (n=1 to 8) are in good agreement with the values obtained numerically by Singh and Varshni. 相似文献
10.
Zhongzhi Zhang Alafate Julaiti Baoyu Hou Hongjuan Zhang Guanrong Chen 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,84(4):691-697
In this paper, by using two different techniques we derive an explicit formula for the
mean first-passage time (MFPT) between any pair of nodes on a general undirected network,
which is expressed in terms of eigenvalues and eigenvectors of an associated matrix
similar to the transition matrix. We then apply the formula to derive a lower bound for
the MFPT to arrive at a given node with the starting point chosen from the stationary
distribution over the set of nodes. We show that for a correlated scale-free network of
size N with a degree distribution
P(d) ∼ d
−γ
,
the scaling of the lower bound is
N
1−1/γ
. Also, we
provide a simple derivation for an eigentime identity. Our work leads to a comprehensive
understanding of recent results about random walks on complex networks, especially on
scale-free networks. 相似文献
11.
We develop a method for calculating diamagnetic susceptibilities based on higher-order perturbation theory for the wave function
and energy of the excited states of the hydrogen atom with degeneracy of arbitrary multiplicity. We derive analytical expressions
for third-order matrix elements in the spherical states |nlm〉 with fixed principal quantum number n and magnetic quantum number m. The formulas for the susceptibilities of doubly degenerate levels are represented in the form of radical-fractional relationships
containing polynomials in the principal quantum number. We establish the existence of a monotonic interdependence between
the absolute values of susceptibilities of the first three orders. We also present the results of numerical calculations for
the states with n⩽6 and m⩽3 mixed by the field. Finally, for Rydberg states with large n and small m we detect the existence of a discontinuity in the interdependence of the susceptibilities at the boundary between the doublet
and equidistant parts of the spectrum of diamagnetic sublevels with opposite parities.
Zh. éksp. Teor. Fiz. 116, 838–857 (September 1999) 相似文献
12.
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
13.
14.
We consider a random walk on the support of an ergodic simple point process on , d ≥ 2, furnished with independent energy marks. The jump rates of the random walk decay exponentially in the jump length and
depend on the energy marks via a Boltzmann–type factor. This is an effective model for the phonon–induced hopping of electrons
in disordered solids in the regime of strong Anderson localization. Under some technical assumption on the point process we
prove an upper bound for the diffusion matrix of the random walk in agreement with Mott law. A lower bound for d ≥ 2 in agreement with Mott law was proved in [8]. 相似文献
15.
B. Lobe W. Janke K. Binder 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,7(2):283-291
We analyze recently extended high-temperature series expansions for the “Edwards-Anderson” spin-glass susceptibility of the
p-state Potts glass model on d-dimensional hypercubic lattices for the case of a symmetric bimodal distribution of ferro- and antiferromagnetic nearest-neighbor
couplings . In these star-graph expansions up to order 22 in the inverse temperature , the number of Potts states p and the dimension d are kept as free parameters which can take any value. By applying several series analysis techniques to the new series expansions,
this enabled us to determine the critical coupling Kc and the critical exponent of the spin-glass susceptibility in a large region of the two-dimensional (p,d)-parameter space. We discuss the thus obtained information with emphasis on the lower and upper critical dimensions of the
model and present a careful comparison with previous estimates for special values of p and d.
Received: 25 May 1998 / Revised and Accepted: 11 August 1998 相似文献
16.
Peter Grassberger 《Journal of statistical physics》2009,136(2):399-404
We simulate loop-erased random walks on simple (hyper-)cubic lattices of dimensions 2, 3 and 4. These simulations were mainly
motivated to test recent two loop renormalization group predictions for logarithmic corrections in d=4, simulations in lower dimensions were done for completeness and in order to test the algorithm. In d=2, we verify with high precision the prediction D=5/4, where the number of steps n after erasure scales with the number N of steps before erasure as n∼N
D/2. In d=3 we again find a power law, but with an exponent different from the one found in the most precise previous simulations:
D=1.6236±0.0004. Finally, we see clear deviations from the naive scaling n∼N in d=4. While they agree only qualitatively with the leading logarithmic corrections predicted by several authors, their agreement
with the two-loop prediction is nearly perfect. 相似文献
17.
We study occurrences of patterns on clusters of size n in random fields on ℤ
d
. We prove that for a given pattern, there is a constant a>0 such that the probability that this pattern occurs at most na times on a cluster of size n is exponentially small. Moreover, for random fields obeying a certain Markov property, we show that the ratio between the
numbers of occurrences of two distinct patterns on a cluster is concentrated around a constant value. This leads to an elegant
and simple proof of the ratio limit theorem for these random fields, which states that the ratio of the probabilities that
the cluster of the origin has sizes n+1 and n converges as n→∞. Implications for the maximal cluster in a finite box are discussed. 相似文献
18.
C. Borgs J. T. Chayes H. Kesten J. Spencer 《Communications in Mathematical Physics》2001,224(1):153-204
We address the question of finite-size scaling in percolation by studying bond percolation in a finite box of side length
n, both in two and in higher dimensions. In dimension d= 2, we obtain a complete characterization of finite-size scaling. In dimensions d>2, we establish the same results under a set of hypotheses related to so-called scaling and hyperscaling postulates which
are widely believed to hold up to d= 6.
As a function of the size of the box, we determine the scaling window in which the system behaves critically. We characterize
criticality in terms of the scaling of the sizes of the largest clusters in the box: incipient infinite clusters which give
rise to the infinite cluster. Within the scaling window, we show that the size of the largest cluster behaves like n
d
π
n
, where π
n
is the probability at criticality that the origin is connected to the boundary of a box of radius n. We also show that, inside the window, there are typically many clusters of scale n
d
π
n
, and hence that “the” incipient infinite cluster is not unique. Below the window, we show that the size of the largest cluster
scales like ξ
d
πξ log(n/ξ), where ξ is the correlation length, and again, there are many clusters of this scale. Above the window, we show that the
size of the largest cluster scales like n
d
P
∞, where P
∞ is the infinite cluster density, and that there is only one cluster of this scale. Our results are finite-dimensional analogues
of results on the dominant component of the Erdős–Rényi mean-field random graph model.
Received: 6 December 2000 / Accepted: 25 May 2001 相似文献
19.
Hatem Najar Samir Ben Hariz Mounir Ben Salah 《Mathematical Physics, Analysis and Geometry》2010,13(1):19-28
In this study we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional
straight strip of width d. We impose the Neumann boundary condition on a disc window of radius a and Dirichlet boundary conditions on the remained part of the boundary of the strip. We prove that such system exhibits discrete
eigenvalues below the essential spectrum for any a > 0. We give also a numeric estimation of the number of discrete eigenvalue as a function of
\fracad\frac{a}{d}. When a tends to the infinity, the asymptotic of the eigenvalue is given. 相似文献
20.
Motivated by the recent discovery of a quantum Chernoff theorem for asymptotic state discrimination, we investigate the distinguishability
of two bipartite mixed states under the constraint of local operations and classical communication (LOCC), in the limit of
many copies. While for two pure states a result of Walgate et al. shows that LOCC is just as powerful as global measurements, data hiding states (DiVincenzo et al.) show that locality can impose severe restrictions on the distinguishability of even orthogonal states. Here we determine
the optimal error probability and measurement to discriminate many copies of particular data hiding states (extremal d × d Werner states) by a linear programming approach. Surprisingly, the single-copy optimal measurement remains optimal for n copies, in the sense that the best strategy is measuring each copy separately, followed by a simple classical decision rule.
We also put a lower bound on the bias with which states can be distinguished by separable operations. 相似文献