共查询到20条相似文献,搜索用时 31 毫秒
1.
Abdullah Algin Metin Arik Deniz Kocabicakoglu 《International Journal of Theoretical Physics》2008,47(5):1322-1332
We construct a two-parameter deformed SUSY algebra for the system of n ordinary fermions and n(q
1,q
2)-deformed bosons called Fibonacci oscillators with
-symmetry. We then analyze the Fock space representation of the algebra constructed. We obtain the total deformed Hamiltonian
and the energy levels together with their degeneracies for the system. We also consider some physical applications of the
Fibonacci oscillators with
-symmetry, and discuss the main reasons to consider two distinct deformation parameters. 相似文献
2.
Abdullah Algin 《International Journal of Theoretical Physics》2009,48(1):71-84
We discuss the algebras, representations, and thermodynamics of quantum group bosonic gas models with two different symmetries:
GL
p,q
(2) and
. We establish the nature of the basic numbers which follow from these GL
p,q
(2)- and
-invariant bosonic algebras. The Fock space representations of both of these quantum group invariant bosonic oscillator algebras
are analyzed. It is concisely shown that these two quantum group invariant bosonic particle gases have different algebraic
and high-temperature thermo-statistical properties. 相似文献
3.
C. Tsallis 《The European Physical Journal A - Hadrons and Nuclei》2009,40(3):257-266
The thermodynamical concept of entropy was introduced by Clausius in 1865 in order to construct the exact differential dS =
Q/T , where
Q is the heat transfer and the absolute temperature T its integrating factor. A few years later, in the period 1872-1877, it was shown by Boltzmann that this quantity can be expressed
in terms of the probabilities associated with the microscopic configurations of the system. We refer to this fundamental connection
as the Boltzmann-Gibbs (BG) entropy, namely (in its discrete form) , where k is the Boltzmann constant, and {p
i} the probabilities corresponding to the W microscopic configurations (hence ∑W
i=1
p
i = 1 . This entropic form, further discussed by Gibbs, von Neumann and Shannon, and constituting the basis of the celebrated
BG statistical mechanics, is additive. Indeed, if we consider a system composed by any two probabilistically independent subsystems A and B (i.e., , we verify that . If a system is constituted by N equal elements which are either independent or quasi-independent (i.e., not too strongly correlated, in some specific nonlocal sense), this additivity guarantees SBG to be extensive in the thermodynamical sense, i.e., that in the N ≫ 1 limit. If, on the contrary, the correlations between the N elements are strong enough, then the extensivity of SBG is lost, being therefore incompatible with classical thermodynamics. In such a case, the many and precious relations described
in textbooks of thermodynamics become invalid. Along a line which will be shown to overcome this difficulty, and which consistently
enables the generalization of BG statistical mechanics, it was proposed in 1988 the entropy . In the context of cybernetics and information theory, this and similar forms have in fact been repeatedly introduced before
1988. The entropic form Sq is, for any q
1 , nonadditive. Indeed, for two probabilistically independent subsystems, it satisfies . This form will turn out to be extensive for an important class of nonlocal correlations, if q is set equal to a special value different from unity, noted qent (where ent stands for entropy . In other words, for such systems, we verify that , thus legitimating the use of the classical thermodynamical relations. Standard systems, for which SBG is extensive, obviously correspond to q
ent = 1 . Quite complex systems exist in the sense that, for them, no value of q exists such that Sq is extensive. Such systems are out of the present scope: they might need forms of entropy different from Sq, or perhaps --more plainly-- they are just not susceptible at all for some sort of thermostatistical approach. Consistently
with the results associated with Sq, the q -generalizations of the Central Limit Theorem and of its extended Lévy-Gnedenko form have been achieved. These recent theorems
could of course be the cause of the ubiquity of q -exponentials, q -Gaussians and related mathematical forms in natural, artificial and social systems. All of the above, as well as presently
available experimental, observational and computational confirmations --in high-energy physics and elsewhere-- are briefly
reviewed. Finally, we address a confusion which is quite common in the literature, namely referring to distinct physical mechanisms
versus distinct regimes of a single physical mechanism.
This paper is part of the Topical Issue Statistical Power Law Tails in High-Energy Phenomena. 相似文献
4.
5.
For weakly non ergodic systems, the probability density function of a time average observable
is
where
is the value of the observable when the system is in state j=1,…L. p
j
eq is the probability that a member of an ensemble of systems occupies state j in equilibrium. For a particle undergoing a fractional diffusion process in a binding force field, with thermal detailed
balance conditions, p
j
eq is Boltzmann’s canonical probability. Within the unbiased sub-diffusive continuous time random walk model, the exponent 0<α<1 is the anomalous diffusion exponent 〈x
2〉∼t
α
found for free boundary conditions. When α→1 ergodic statistical mechanics is recovered
. We briefly discuss possible physical applications in single particle experiments. 相似文献
6.
V. Schwämmle F. D. Nobre C. Tsallis 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,66(4):537-546
The stability of q-Gaussian distributions as particular solutions of the
linear diffusion equation and its generalized nonlinear form, , the porous-medium equation, is investigated through both numerical
and analytical approaches. An analysis of the kurtosis of the distributions strongly suggests that an initial q-Gaussian, characterized by an index qi, approaches asymptotically the
final, analytic solution of the porous-medium equation, characterized by an index q, in such a way that the relaxation rule for
the kurtosis evolves in time according to a q-exponential, with a relaxation index qrel ≡qrel(q). In some cases, particularly when one attempts to transform an infinite-variance distribution (qi ≥ 5/3) into a finite-variance
one (q < 5/3), the relaxation towards the asymptotic solution may occur very slowly in time. This fact might shed some light
on the slow relaxation, for some long-range-interacting many-body Hamiltonian systems, from long-standing quasi-stationary
states to the ultimate thermal equilibrium
state. 相似文献
7.
A recent investigation of the possibility of having a
-symmetric periodic potential in an optical lattice stimulated the urge to generalize non-hermitian quantum mechanics beyond
the case of commutative space. We thus study non-hermitian quantum systems in non-commutative space as well as a
-symmetric deformation of this space. Specifically, a
-symmetric harmonic oscillator together with an iC(x
1+x
2) interaction are discussed in this space, and solutions are obtained. We show that in the
deformed non-commutative space the Hamiltonian may or may not possess real eigenvalues, depending on the choice of the non-commutative
parameters. However, it is shown that in standard non-commutative space, the iC(x
1+x
2) interaction generates only real eigenvalues despite the fact that the Hamiltonian is not
-symmetric. A complex interacting anisotropic oscillator system also is discussed. 相似文献
8.
In this paper, an error in the proof of Theorem 4.9 in Gudder’s paper (Int. J. Theor. Phys. 47(1):268–279, 2008) is pointed out and it is proved that if
such that E
i
∈ℂI∖{0} and E
j
∉ℂI for some i,j in {1,2,…,n}, then
.
This subject is supported by the NNSF of China (No. 10571113, 10871224). 相似文献
9.
Alexis Pokrovski 《Mathematical Physics, Analysis and Geometry》2007,10(3):197-203
Let be the spectrum of in L
2(ℝ), where q is an even almost-periodic complex-valued function with bounded primitive and derivative. It is known that , where is the spectrum of the unperturbed operator. Suppose that the asymptotic approximation to the first asymptotic correction
is given. We prove the formula that recovers the frequencies and the Fourier coefficients of q in terms of Δμ
n
.
相似文献
10.
A. Prats Ferrer B. Eynard P. Di Francesco J.-B. Zuber 《Journal of statistical physics》2007,129(5-6):885-935
The Harish-Chandra correlation functions, i.e. integrals over compact groups of invariant monomials
with the weight exp tr (X
Ω
Y
Ω
†
) are computed for the orthogonal and symplectic groups. We proceed in two steps. First, the integral over the compact group
is recast into a Gaussian integral over strictly upper triangular complex matrices (with some additional symmetries), supplemented
by a summation over the Weyl group. This result follows from the study of loop equations in an associated two-matrix integral
and may be viewed as the adequate version of Duistermaat–Heckman’s theorem for our correlation function integrals. Secondly,
the Gaussian integration over triangular matrices is carried out and leads to compact determinantal expressions. 相似文献
11.
M. Bisset N. Kersting J. Li F. Moortgat S. Moretti Q. L. Xie 《The European Physical Journal C - Particles and Fields》2006,45(2):477-492
Processes of the form pp → anything → XiXj →
+
+ notE are studied via a technique that may be viewed as an adaptation of time-honoured Dalitz plot analyses. Xi and Xj are new heavy states (with i, j =1, . . .,n), which may be identical or distinct; and
and
are necessarily distinct standard model (SM) fermion pairs whose invariant masses can be measured. A Dalitz-like plot of
said invariant masses,
versus
, exhibits a topology connected to the masses and specific decay chains of Xi and Xj. Aside from relatively minor details, observed patterns consist of a collection of box and wedge shapes. This collection
is model-dependent: comparison of the observed pattern to the possibilities for a specific model yields information on which
new particle pair combinations are actually being produced, information beyond that extractable from conventional one-dimensional
invariant mass distributions. The technique is illustrated via application to the minimal supersymmetric standard model (MSSM)
process pp →
→ e+e- + μ+μ- notE. Here the heavy states are neutralinos
(i = 2,3,4) - note that
is excluded - which are produced in gluino/squark (
/
) cascade decay chains. Even with fairly modest expectations for the LHC performance during the first few years, this method
still provides substantial insight into the neutralino mass spectrum and couplings if gluino/squark masses are relatively
low (≃ 400 GeV).
Arrival of the final proofs: 29 November 2005 相似文献
12.
We examine by molecular dynamics simulations the relaxation of polymer-solvent mixtures close to the glass transition. The
simulations employ a coarse-grained model in which polymers are represented by bead-spring chains and solvent particles by
monomers. The interaction parameters between polymer and solvent are adjusted such that mixing is favored. We find that the
mixtures have one glass transition temperature T
g or critical temperature T
c of mode-coupling theory (MCT). Both T
g and T
c (> T
g decrease with increasing solvent concentration . The decrease is linear for the concentrations studied (up to = 25%. Above T
c we explore the structure and relaxation of the polymer-solvent mixtures on cooling. We find that, if the polymer solution
is compared to the pure polymer melt at the same T, local spatial correlations on the length scale of the first peak of the static structure factor S(q) are reduced. This difference between melt and solution is largely removed when comparing the S(q) of both systems at similar distance to the respective T
c. Near T
c we investigate dynamic correlation functions, such as the incoherent intermediate scattering function (t), mean-square displacements of the monomers and solvent particles, two non-Gaussian parameters, and the probability distribution
P(ln r;t) of the logarithm of single-particle displacements. In accordance with MCT we find, for instance, that (t) obeys the time-temperature superposition principle and has relaxation times which are compatible with a power law increase close (but not too close) to T
c. In divergence to MCT, however, the increase of depends on the wavelength q, small q values having weaker increase than large ones. This decoupling of local and large-length scale relaxation could be related
to the emergence of dynamic heterogeneity at low T. In the time window of the relaxation an analysis of P(ln r;t) reveals a double-peak structure close to T
c. The first peak correponds to “slow” particles (monomer or solvent) which have not moved much farther than 10% of their diameter
in time t, whereas the second occurs at distances of the order of the particle diameter. These “fast” particles have succeeded in leaving
their nearest-neighbor cage in time t. The simulation thus demonstrates that large fluctuations in particle mobility accompany the final structural relaxation
of the cold polymer solution in the vicinity of the extrapolated T
c. 相似文献
13.
We show that the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen “exchangeability”
(i.e., invariance of the joint distribution of the random variables under the action of the permutation group) to invariance
under the action of the quantum permutation group. More precisely, for an infinite sequence of noncommutative random variables
, we prove that invariance of the joint distribution of the x
i
’s under quantum permutations is equivalent to the fact that the x
i
’s are identically distributed and free with respect to the conditional expectation onto the tail algebra of the x
i
’s.
Research supported by Discovery and LSI grants from NSERC (Canada) and by a Killam Fellowship from the Canada Council for
the Arts. 相似文献
14.
Let p≥2, n
1≤⋅⋅⋅≤n
p
be positive integers and
be independent planar Brownian motions started uniformly on the boundary of the unit circle. We define a p-fold intersection exponent ς
p
(n
1,…,n
p
), as the exponential rate of decay of the probability that the packets
, i=1,…,p, have no joint intersection. The case p=2 is well-known and, following two decades of numerical and mathematical activity, Lawler et al. (Acta Math. 187:275–308,
2001) rigorously identified precise values for these exponents. The exponents have not been investigated so far for p>2. We present an extensive mathematical and numerical study, leading to an exact formula in the case n
1=1, n
2=2, and several interesting conjectures for other cases. 相似文献
15.
For classicalN-particle systems with pair interactionN
–1
ø(q
i–q
i) the Vlasov dynamics is shown to be thew*-limit asN. Propagation of molecular chaos holds in this limit, and the fluctuations of intensive observables converge to a Gaussian stochastic process. 相似文献
16.
A search for lepton-flavor-violating interactions
and
has been performed with the ZEUS detector using the entire HERA I data sample, corresponding to an integrated luminosity
of
. The data were taken at center-of-mass energies,
, of 300 and
. No evidence of lepton-flavor violation was found, and constraints were derived on leptoquarks (LQs) that could mediate such
interactions. For LQ masses below
, limits were set on
, where
is the coupling of the LQ to an electron and a first-generation quark q1, and
is the branching ratio of the LQ to the final-state lepton
(μ or
) and a quark q. For LQ masses much larger than
, limits were set on the four-fermion interaction term
for LQs that couple to an electron and a quark
and to a lepton
and a quark
, where
and
are quark generation indices. Some of the limits are also applicable to lepton-flavor-violating processes mediated by squarks
in R-Parity-violating supersymmetric models. In some cases, especially when a higher-generation quark is involved and for the
process
, the ZEUS limits are the most stringent to date.
Received: 1 April 2005, Revised: 13 July 2005, Published online: 18 October 2005 相似文献
17.
《The European Physical Journal C - Particles and Fields》2007,51(2):249-269
In the reaction e+e-→WW→(q1q̄2)(q3q̄4) the usual hadronization models treat the colour singlets q1q̄2 and q3q̄4 coming from two W bosons independently. However, since the final state partons may coexist in space and time, cross-talk
between the two evolving hadronic systems may be possible during fragmentation through soft gluon exchange. This effect is
known as colour reconnection. In this article the results of the investigation of colour reconnection effects in fully hadronic
decays of W pairs in DELPHI at LEP are presented. Two complementary analyses were performed, studying the particle flow between
jets and W mass estimators, with negligible correlation between them, and the results were combined and compared to models.
In the framework of the SK-I model, the value for its κ parameter most compatible with the data was found to be: κSK-I=2.2+2.5
-1.3 corresponding to the probability of reconnection to be in the range at 68% confidence level with its best value at 0.52. 相似文献
18.
E. Epelbaum Ulf-G Meißner W. Glöckle 《The European Physical Journal A - Hadrons and Nuclei》2003,18(2-3):499-502
We investigate the behavior of the nuclear force as a function of the light-quark masses m
q
in the framework of chiral effective field theory at next-to-leading order. The unknown m
q
-dependent short-range contribution is estimated by means of dimensional analysis. We calculate various observables for different values of m
q
. We found no new bound states and a larger deuteron binding energy,
MeV, in the chiral limit.Received: 30 September 2002, Published online: 22 October 2003PACS:
11.30.Rd Chiral symmetries - 13.75.Cs Nucleon-nucleon interactions (including antinucleons, deuterons, etc.) - 21.30.Cb Nuclear forces in vacuum - 21.30.Fe Forces in hadronic systems and effective interactions 相似文献
19.
We obtain exact results in α′ for open and closed A-model topological string amplitudes on a large class of toric Calabi-Yau threefolds by using their correspondence with five
dimensional gauge theories. The toric Calabi-Yaus that we analyze are obtained as minimal resolution of cones over Y
p,q
manifolds and give rise via M-theory compactification to SU(p) gauge theories on . As an application we present a detailed study of the local case and compute open and closed genus zero Gromov-Witten invariants of the orbifold. We also display the modular structure of the topological wave function and give predictions for higher genus amplitudes.
The mirror curve in this case is the spectral curve of the relativistic A
1 Toda chain. Our results also indicate the existence of a wider class of relativistic integrable systems associated to generic
Y
p,q
geometries. 相似文献