共查询到20条相似文献,搜索用时 31 毫秒
1.
V.F. Müller 《Nuclear Physics B》1982,205(4):578-584
An upper and a lower bound for the free energy density of a lattice gauge teory with compact gauge group are derived, valid for all values of β. For large β the first two terms of the asymptotic expansions of these bounds coincide, thus determining the corresponding terms of the free energy density. Moreover the gauge groups U(N) and SU(N) are treated explicitly. 相似文献
2.
Fu-Gang Zhang 《理论物理通讯》2022,74(1):15102
In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums of coherence are obtained.However,the above results cannot be verified directly for any α∈(0,1/2).Hence,we only consider the special case of α=1/n+1,where n is a positive integer,and we obtain the upper and lower bounds.By comparing the upper and lower bounds,we find that the upper bound is equal to the lower bound for the special α=1/2,and the differences between the upper and the lower bounds will increase as α increases.Furthermore,we discuss the tendency of the sum of coherence,and find that it has the same tendency with respect to the different θ or φ,which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy. 相似文献
3.
N.K. Vitanov 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(2):349-355
We present the theory of the multi--solutions of the variational problem for the upper bounds on the convective heat transport in a heated from below horizontal
fluid layer with rigid lower boundary and stress-free upper boundary. A sequence of upper bounds on the convective heat transport
is obtained. The highest bound is between the bounds for the case of a fluid layer with two rigid boundaries and for the case of a fluid layer with two stress-free boundaries. As an additional result of the presented theory we obtain
small corrections of the boundary layer thicknesses of the optimum fields for the case of fluid layer with two rigid boundaries.
These corrections lead to systematically lower upper bounds on the convective heat transport in comparison to the bounds obtained
in [5].
Received 29 September 1999 相似文献
4.
S. Franz T. Garel H. Orland 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,11(3):463-468
We consider a model of two (fully) compact polymer chains, coupled through an attractive interaction. These compact chains
are represented by Hamiltonian paths (HP), and the coupling favors the existence of common bonds between the chains. We use
a (n=0 component) spin representation for these paths, and we evaluate the resulting partition function within a homogeneous saddle
point approximation. For strong coupling (i.e. at low temperature), one finds a phase transition towards a “frozen” phase where one chain is completely adsorbed onto the
other. By performing a Legendre transform, we obtain the probability distribution of overlaps. The fraction of common bonds
between two HP, i.e. their overlap q, has both lower () and upper () bounds. This means in particular that two HP with overlap greater than coincide. These results may be of interest in (bio)polymers and in optimization problems.
Received 4 December 1998 and Received in final form 10 March 1999 相似文献
5.
M. van den Berg T. C. Dorlas J. T. Lewis J. V. Pulé 《Communications in Mathematical Physics》1990,128(2):231-245
This completes our study of the equilibrium thermodynamics of the Huang-Yang-Luttinger model of a boson gas with a hard-sphere repulsion. In an earlier paper we obtained a lower bound on the pressure, but our proof of an upper bound held only for a truncated version of the model. In this paper we establish an upper bound on the pressure in the full model; the upper and lower bounds coincide and provide a variational formula for the pressure. The proof relies on recent second-level large deviation results for the occupation measure of the free boson gas. 相似文献
6.
N.K. Vitanov 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,23(2):249-266
By means of the Howard-Busse method of the optimum theory of turbulence we obtain upper bounds on the convective heat transport
in a horizontal fluid layer heated from below and rotating about a vertical axis. We consider the interval of large Taylor
numbers where the intermediate layers of the optimum fields expand in the direction of the corresponding internal layers.
We consider the 1 - α-solution of the arising variational problem for the cases of rigid-stress-free, stress-free, and rigid
boundary conditions. For each kind of boundary condition we discuss four cases: two cases where the boundary layers are thinner
than the Ekman layers of the optimum field and two cases where the boundary layers are thicker than the Ekman layers. In most
cases we use an improved solution of the Euler-Lagrange equations of the variational problem for the intermediate layers of
the optimum fields. This solution leads to corrections of the thicknesses of the boundary layers of the optimum fields and
to lower upper bounds on the convective heat transport in comparison to the bounds obtained by Chan [J. Fluid Mech. 64, 477 (1974)] and Hunter and Riahi [J. Fluid Mech. 72, 433 (1975)]. Compared to the existing experimental data for the case of a fluid layer with rigid boundaries the corresponding
upper bounds on the convective heat transport is less than two times larger than the experimental results, the corresponding
upper bound on the convective heat transport, obtained by Hunter and Riahi is about 10% higher than the bound obtained in
this article. When Rayleigh number and Taylor number are high enough the upper bound on the convective heat transport ceases
to depend on the boundary conditions.
Received 30 January 2001 and Received in final form 28 May 2001 相似文献
7.
We study irreversible A-B reaction kinetics at a fixed interface separating two immiscible bulk phases, A and B. Coupled equations
are derived for the hierarchy of many-body correlation functions. Postulating physically motivated bounds, closed equations
result without the need for ad hoc decoupling approximations. We consider general dynamical exponent z, where is the rms diffusion distance after time t. At short times the number of reactions per unit area, , is 2nd order in the far-field reactant densities . For spatial dimensions dabove a critical value , simple mean field (MF) kinetics pertain, where Qb is the local reactivity. For low dimensions , this MF regime is followed by 2nd order diffusion controlled (DC) kinetics, , provided . Logarithmic corrections arise in marginal cases. At long times, a cross-over to 1st order DC kinetics occurs: . A density depletion hole grows on the more dilute A side. In the symmetric case (), when the long time decay of the interfacial reactant density, , is determined by fluctuations in the initial reactant distribution, giving . Correspondingly, A-rich and B-rich regions develop at the interface analogously to the segregation effects established by
other authors for the bulk reaction . For fluctuations are unimportant: local mean field theory applies at the interface (joint density distribution approximating
the product of A and B densities) and . We apply our results to simple molecules (Fickian diffusion, z=2) and to several models of short-time polymer diffusion (z>2).
Received 8 June 1998 and Received in final form 10 September 1999 相似文献
8.
A. R.R. Carvalho F. Mintert S. Palzer A. Buchleitner 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2007,41(2):425-432
We investigate the time evolution of entanglement for bipartite systems of
arbitrary dimensions under the influence of decoherence. For qubits, we
determine the precise entanglement decay rates under different
system-environment couplings, including finite temperature effects. For qudits, we show how
to obtain upper bounds for the decay rates and also present exact solutions
for various classes of states. 相似文献
9.
C. S. Yu X. X. Yi H. S. Song 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,49(2):273-278
For a tripartite pure state superposed by two individual states, the bipartitely shared entanglement can always be achieved
by local measurements of the third party. Consider the different aims of the third party, i.e. maximizing or minimizing the
bipartitely shared entanglement, we find bounds on both the possible bipartitely shared entanglement of the superposition
state in terms of the corresponding entanglement of the two states being superposed. In particular, by choosing the concurrence
as bipartite entanglement measure, we obtain calculable bounds for tripartite (2 ⊗ 2 ⊗ n)-dimensional cases. 相似文献
10.
This Letter considers the problem of delay-range-dependent stability for fuzzy bi-directional associative memory (BAM) neural networks with time-varying interval delays. Based on Lyapunov-Krasovskii theory, the delay-range-dependent stability criteria are derived in terms of linear matrix inequalities (LMIs). By constructing new Lyapunov-Krasovskii functional, stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using some advanced techniques for achieving delay dependence. A numerical example is given to illustrate the effectiveness of the proposed method. 相似文献
11.
Alexey E. Rastegin 《Mathematical Physics, Analysis and Geometry》2013,16(3):213-228
Pinsker’s and Fannes’ type bounds on the Tsallis relative entropy are derived. The monotonicity property of the quantum f -divergence is used fot its estimation from below. For order $\alpha \in (0,1)$ , a family of lower bounds of Pinsker type is obtained. For $\alpha >1$ and the commutative case, upper continuity bounds on the relative entropy in terms of the minimal probability in its second argument are derived. Both the lower and upper bounds presented are reformulated for the case of Rényi’s entropies. The Fano inequality is extended to Tsallis’ entropies for all $\alpha >0$ . The deduced bounds on the Tsallis conditional entropy are used to obtain inequalities of Fannes’ type. 相似文献
12.
David Ruelle 《Communications in Mathematical Physics》1982,87(2):287-302
For spatially extended conservative or dissipative physical systems, it appears natural that a density of characteristic exponents per unit volume should exist when the volume tends to infinity. In the case of a turbulent viscous fluid, however, this simple idea is complicated by the phenomenon of intermittency. In the present paper we obtain rigorous upper bounds on the distribution of characteristic exponents in terms of dissipation. These bounds have a reasonable large volume behavior. For two-dimensional fluids a particularly striking result is obtained: the total information creation is bounded above by a fixed multiple of the total energy dissipation (at fixed viscosity). The distribution of characteristic exponents is estimated in an intermittent model of turbulence (see [7]), and it is found that a change of behavior occurs at the valueD=2.6 of the self-similarity dimension. 相似文献
13.
Upper and lower bounds are given for the three lowest frequencies of vibration of clamped rectangular orthotropic plates. The bounds were obtained by using a recently developed method which gives estimates for the vibrational frequencies in terms of easily evaluated integrals of trial functions. Important features of the method are that rigorous, improvable upper and lower bounds on the frequencies are obtained and that the trial functions need not satisfy any boundary conditions. 相似文献
14.
K.-H. Ma C. S. Yu H. S. Song 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2010,59(2):317-320
By a variational definition of the entanglement measure – negativity, we derive an upper bound of negativity of superpositions
in terms of the negativities of the quantum states being superposed. It is shown that the upper bound has a simple formulation.
In particular, in many cases the upper bound is tighter than the previous bounds. 相似文献
15.
Rigorous upper and lower bounds are presented for the frequencies of vibration of a thin elastic plate reinforced by an elastically attached rib. This study has two purposes: the first is to indicate how a method for lower bounds can be applied to simple built-up structures and the second is to demonstrate the effectiveness of the method in a relatively easy but useful application. 相似文献
16.
This paper deals with the specific construction of binary low-density parity-check (LDPC) codes. We derive lower bounds on the error exponents for these codes transmitted over the memoryless binary symmetric channel (BSC) for both the well-known maximum-likelihood (ML) and proposed low-complexity decoding algorithms. We prove the existence of such LDPC codes that the probability of erroneous decoding decreases exponentially with the growth of the code length while keeping coding rates below the corresponding channel capacity. We also show that an obtained error exponent lower bound under ML decoding almost coincide with the error exponents of good linear codes. 相似文献
17.
We compute the pressure of the random energy model (REM) and generalized random energy model (GREM) by establishing variational
upper and lower bounds. For the upper bound, we generalize Guerra’s “broken replica symmetry bounds,” and identify the random
probability cascade as the appropriate random overlap structure for the model. For the REM the lower bound is obtained, in
the high temperature regime using Talagrand’s concentration of measure inequality, and in the low temperature regime using
convexity and the high temperature formula. The lower bound for the GREM follows from the lower bound for the REM by induction.
While the argument for the lower bound is fairly standard, our proof of the upper bound is new. 相似文献
18.
Michele Pasquini Giovanni Paladin Maurizio Serva 《Journal of statistical physics》1995,80(1-2):357-373
We find analytic upper and lower bounds of the Lyapunov exponents of the product of random matrices related to the one-dimensional disordered Ising model, using a deterministic map which transforms the original system into a new one with smaller average couplings and magnetic fields. The iteration of the map gives bounds which estimate the Lyapunov exponents with increasing accuracy. We prove, in fact, that both the upper and the lower bounds converge to the Lyapunov exponents in the limit of infinite iterations of the map. A formal expression of the Lyapunov exponents is thus obtained in terms of the limit of a sequence. Our results allow us to introduce a new numerical procedure for the computation of the Lyapunov exponents which has a precision higher than Monte Carlo simulations. 相似文献
19.
The steady state of a system of independent particles which undergo elastic collisions can be expressed in terms of the absorption probabilities of the associated Markov process. For the slab albedo problem, this representation enables the application of probabilistic methods to obtain explicit upper and lower bounds on the steady-state density. In particular, the bounds prove the 1/L, decrease of the steady-state flux as a function of the slab widthL (Fick's law).Supported in part by U.S. National Science Foundation grant MCS 75-21684 A02.On leave of absence from Fachbereich Physik, UniversitÄt Mönchen. Work supported by a DFG research fellowship. 相似文献
20.
Large spin systems as given by magnetic macromolecules or two-dimensional spin arrays rule out an exact diagonalization of
the Hamiltonian. Nevertheless, it is possible to derive upper and lower bounds of the minimal energies, i.e. the smallest energies for a given total spin S. The energy bounds are derived under additional assumptions on the topology of the coupling between the spins. The upper
bound follows from “n-cyclicity", which roughly means that the graph of interactions can be wrapped round a ring with n vertices. The lower bound improves earlier results and follows from “n-homogeneity", i.e. from the assumption that the set of spins can be decomposed into n subsets where the interactions inside and between spins of different subsets fulfill certain homogeneity conditions. Many
Heisenberg spin systems comply with both concepts such that both bounds are available. By investigating small systems which
can be numerically diagonalized we find that the upper bounds are considerably closer to the true minimal energies than the
lower ones.
Received 22 October 2002 / Received in final form 4 April 2003 Published online 20 June 2003
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ID="a"e-mail: jschnack@uos.de 相似文献