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1.
Hyun Jae Yoo 《Journal of statistical physics》2007,126(2):325-354
Given a positive definite, bounded linear operator A on the Hilbert space
0≔l
2(E), we consider a reproducing kernel Hilbert space
+ with a reproducing kernel A(x,y). Here E is any countable set and A(x,y), x,y∊ E, is the representation of A w.r.t. the usual basis of
0. Imposing further conditions on the operator A, we also consider another reproducing kernel Hilbert space
− with a kernel function B(x,y), which is the representation of the inverse of A in a sense, so that
−⊃
0⊃
+ becomes a rigged Hilbert space. We investigate the ratios of determinants of some partial matrices of A and B. We also get a variational principle on the limit ratios of these values. We apply this relation to show the Gibbsianness
of the determinantal point process (or fermion point process) defined by the operator A(I+A)−1 on the set E.
2000 Mathematics Subject Classification: Primary: 46E22 Secondary: 60K35 相似文献
2.
A. G. Ramm 《Journal of statistical physics》2007,127(5):915-934
If A
q(β, α, k) is the scattering amplitude, corresponding to a potential , where D⊂ℝ3 is a bounded domain, and is the incident plane wave, then we call the radiation pattern the function , where the unit vector α, the incident direction, is fixed, β is the unit vector in the direction of the scattered wave,
and k>0, the wavenumber, is fixed. It is shown that any function , where S
2 is the unit sphere in ℝ3, can be approximated with any desired accuracy by a radiation pattern: , where ∊ >0 is an arbitrary small fixed number. The potential q, corresponding to A(β), depends on f and ∊, and can be calculated analytically. There is a one-to-one correspondence between the above potential and the density
of the number of small acoustically soft particles D
m⊂ D, 1≤ m≤ M, distributed in an a priori given bounded domain D⊂ℝ3. The geometrical shape of a small particle D
m is arbitrary, the boundary S
m of D
m is Lipschitz uniformly with respect to m. The wave number k and the direction α of the incident upon D plane wave are fixed. It is shown that a suitable distribution of the above particles in D can produce the scattering amplitude , at a fixed k>0, arbitrarily close in the norm of L
2(S
2× S
2) to an arbitrary given scattering amplitude f(α ', α), corresponding to a real-valued potential q∊ L
2(D), i.e., corresponding to an arbitrary refraction coefficient in D.
MSC: 35J05, 35J10, 70F10, 74J25, 81U40, 81V05, 35R30.
PACS: 03.04.Kf. 相似文献
3.
Extensions of Lieb’s Concavity Theorem 总被引:3,自引:1,他引:2
Frank Hansen 《Journal of statistical physics》2006,124(1):87-101
The operator function (A,B)→ Trf(A,B)(K
*)K, defined in pairs of bounded self-adjoint operators in the domain of a function f of two real variables, is convex for every Hilbert Schmidt operator K, if and only if f is operator convex. We obtain, as a special case, a new proof of Lieb’s concavity theorem for the function (A,B)→ TrA
p
K
*
B
q
K, where p and q are non-negative numbers with sum p+q ≤ 1. In addition, we prove concavity of the operator function
in its natural domain D
2(μ1,μ2), cf. Definition 3. 相似文献
4.
The characteristic features of ortho- and para-helium are investigated within the framework of Relativistic Schr?dinger Theory (RST). The emphasis lies on the conceptual level, where the geometric and physical properties of both RST field configurations are inspected in detail. From the geometric point of view, the striking feature consists in the splitting of the
-valued bundle connection
into an abelian electromagnetic part (organizing the electromagnetic interactions between the two electrons) and an exchange part, which is responsible for their exchange interactions. The electromagnetic interactions are mediated by the usual four-potentials A
μ and thus are essentially the same for both types of field configurations, where naturally the electrostatic forces (described by the time component A
0 of A
μ) dominate their magnetostatic counterparts (described by the space part A of A
μ). Quite analogously to this, the exchange forces are as well described in terms of a certain vector potential (B
μ), again along the gauge principles of minimal coupling, so that also the exchange forces split up into an “electric” type (
) and a “magnetic” type (
). The physical difference of ortho- and para-helium is now that the first (ortho-) type is governed mainly by the “electric” kind of exchange forces and therefore is subject to a stronger influence of the exchange phenomenon; whereas the second (para-) type has vanishing “electric” exchange potential (B
0 ≡ 0) and therefore realizes exclusively the “magnetic” kind of interactions (
), which, however, in general are smaller than their “electric” counterparts. The corresponding ortho/para splitting of the helium energy levels is inspected merely in the lowest order of approximation, where it coincides with the Hartree–Fock (HF) approximation. Thus RST may be conceived as a relativistic generalization of the HF approach where the fluid-dynamic character of RST implies many similarities with the density functional theory. 相似文献
5.
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
6.
Gábor Hofer-Szabó 《International Journal of Theoretical Physics》2006,45(7):1308-1322
A pair (A, B) of events in a classical probability measure space (Ω, p) is called exchangeable iff p(A
) = p(
B). Conditionally identical common cause system of size n for the correlation is an n-partition of Ω such that (i) any member of the partition screens the correlation off and (ii) for any member {C
i
}
i ∊ I
of the partition p(A|C
i
) = p(B|C
i
). The common cause system is called proper if p(A|C
i
)≠(A|C
j
) for some i ≠ j. In the paper it is shown that exchangeable correlations be explained by proper conditionally identical common cause systems in the following sense. (i) Given a proper conditionally identical common cause system of size n for the two events A and B in Ω, then the pair (A, B) will be an exchangeable (positively) correlating pair. (ii) Given any exchangeable (positively) correlating pair of events in Ω and given any finite number n > 2, then the probability space can be embedded into a larger probability space in such a way that the larger space contains a proper conditionally identical common cause system of size n for the correlation. 相似文献
7.
The relation between the set of transformations
of the quantum plane and the quantum universal enveloping algebra U
q
(u(2)) is investigated by constructing representations of the factor algebra U
q
(u(2))*
. The noncommuting coordinates of
, on which U
q
(2) * U
q
(2) acts, are realized as q-spinors with respect to each U
q
(u(2)) algebra. The representation matrices of U
q
(2) are constructed as polynomials in these spinor components. This construction allows a derivation of the commutation relations of the noncommuting coordinates of
directly from properties of U
q
(u(2)). The generalization of these results to U
q
(u(n)) and
is also discussed. 相似文献
8.
K. Okikiolu 《Communications in Mathematical Physics》2009,290(3):1025-1031
Let M be a closed surface. For a metric g on M, denote the Laplace-Beltrami operator by Δ = Δ
g
. We define trace , where dA is the area element for g and m(p) is the Robin constant at the point , that is the value of the Green function G(p, q) at q = p after the logarithmic singularity has been subtracted off. Since trace Δ−1 can also be obtained by regularization of the spectral zeta function, it is a spectral invariant. Heuristically it represents
the sum of squares of the wavelengths of the surface. We define the Δ-mass of (M, g) to equal , where is the Laplacian on the round sphere of area A. This is an analog for closed surfaces of the ADM mass from general relativity. We show that if M has positive genus, the minimum of the Δ-mass on each conformal class is negative and attained by a smooth metric. For this
minimizing metric, there is a sharp logarithmic Hardy-Littlewood-Sobolev inequality and a Moser-Trudinger-Onofri type inequality.
The author would like to acknowledge the support of the Institute for Advanced Study. 相似文献
9.
We consider SU
q
(2) covariant
-matrices for the reducible3 1 representation. There are three solutions to the Yang-Baxter equation. They coincide with the previously known
-matrices for SO
q
(3) and SO
q
(3, 1). Also, they are the three
-matrices which can be constructed by using four different SU
q
(2) doublets. Only two of the three
-matrices allow a differential structure on the reducible four-dimensional quantum space. 相似文献
10.
On the basis of the decay couplings f
0 → ππ, K
, ηη, ηη′ found earlier in the study of analytical (IJ
PC
=00++) amplitude in the mass range 450–1900 MeV, we analyze the quark-gluonium content of the resonances f
0(980), f
0(1300), f
0(1500), and f
0(1750) and the broad state f
0(1420
−70
+150
). The K-matrix technique used in the analysis makes it possible to evaluate the quark-gluonium content both for the states with switched-off
decay channels (bare states, f
0
bare
) and for the real resonances. We observe a significant change in the quark-gluonium composition in the evolution from bare
states to real resonances, which is due to the mixing of states in the transitions f
0(m
1) → real mesons → f
0 (m
2) responsible for the decay processes as well. For f
0(980), the analysis confirmed the dominance of q
component, thus proving the n
/s
composition found in the study of the radiative decays. For the mesons f
0(1300), f
0(1500), and f
0(1750), the hadronic decays do not allow one to determine uniquely the n
, s
, and gluonium components, providing relative percentage only. The analysis shows that the broad state f
0(1420
−70
+150
) can mix with the flavor singlet q
component only, which is consistent with gluonium origin of the broad resonance.
From Yadernaya Fizika, Vol. 66, No. 4, 2003, pp. 772–785.
Original English Text Copyright ? 2003 by Anisovich, Nikonov, Sarantsev.
This article was submitted by the authors in English. 相似文献
11.
The spin-fermion model describes a two level quantum system
(spin 1/2) coupled to finitely many free Fermi gas reservoirs
which are in thermal equilibrium at inverse temperatures β
j
. We consider non-equilibrium initial conditions where not all β
j
are the same. It is known that, at small coupling, the combined system
has a unique non-equilibrium steady state (NESS) characterized by strictly sitive entropy production. In this paper we study
linear response in this NESS and prove the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes generated
by temperature differentials.
Dedicated to Jean Michel Combes on the occasion of his sixtyfifth birthday 相似文献
12.
A. Bahraminasab M. Sadegh Movahed S. D. Nasiri A. A. Masoudi Muhammad Sahimi 《Journal of statistical physics》2006,124(6):1471-1490
We carry out an exact analysis of the average frequency ν+
αxi
in the direction x
i
of positiveslope crossing of a given level α such that, h(x, t) − = α, of growing surfaces in spatial dimension d. Here, h(x, t) is the surface height at time t, and is its mean value. We analyze the problem when the surface growth dynamics is governed by the Kardar-Parisi-Zhang (KPZ) equation without surface tension, in the time regime prior to appearance of cusp singularities (sharp valleys), as well as in the random deposition (RD) model. The total number N
+ of such level-crossings with positive slope in all the directions is then shown to scale with time as t
d/2 for both the KPZ equation and the RD model.
PACS number(s): 52.75.Rx, 68.35.Ct 相似文献
13.
Ground-state masses ofq
2
–2 states (true and mock baryonium) are investigated in the framework of a Bethe-Salpeter formalism motivated from QCD. The four-particle system is described by pairwise interactions betweenqq orq
pairs with a spectator approximation for the non-interacting pair. The quark-quark interactions are Coulomb plus harmonic interactions; the harmonic terms have been modified to produce linear confinement for heavier quarks, in agreement with experimental spectra. The confining interaction is proportional to the strong coupling constant
s. Apart from the quark masses, the confining interaction is characterized by three basic parameters: (i) a universal spring constant
0; (ii) a constantC
0/
0
2
, which defines the vacuum structure; (iii) a constantA
0, which provides a smooth transition from quadratic to linear confinement as one goes from light to heavy quark systems. These three constants [
0 = 0.158 GeV;C
0=0.296;A
0=0.0283] have been shown to produce excellent fits to all quarkonia states [q
,q
,Q
] as well as baryon spectra (qqq); thus our predictions forq
2
2 states contain no free parameters. In this model, theL=0 ground states occur in the range 1.8–2 GeV, 2.15–2.3 GeV and 6.72–6.75 GeV foru
2
2,s
2
2 andc
2
2 states, respectively. We discuss the prospects for these states to be seen experimentally. In the case of thes
2
2 state, this is likely to have a rather narrow width, and may correspond to theX(2.22 GeV) meson observed in radiative decays of theJ/ meson. Thec
2
2 state might also be visible as a resonance with an appreciable width.Research supported in part by the National Science Foundation under grant NSF-PHY 86-06364Research supported in part by the U.S. Department of Energy 相似文献
14.
A novel model system is proposed for the study of superconductor-insulator transitions that is a regular lattice whose each
link consists of a Josephson-junction chain of N ≫ 1 junctions in sequence. The theory of such an array is developed for the case of semiclassical junctions with the Josephson
energy E
J
larger compared to the Coulomb energy E
C
= e
2/2C of the junctions. An exact duality transformation is derived that transforms the Hamiltonian of the proposed model into a
standard Hamiltonian of a JJ array. The nature of the ground state is controlled (in the absence of random offset charges)
by the parameter q ≈ N
2 exp
with the superconductive state corresponding to small q < q
c
. The values of q
c
are calculated for magnetic frustrations f = 0 and f = 1/2. The temperature of the superconductive transition T
c
(q) and q < q
c
is estimated for the same values of f. In the presence of strong random offset charges, the T = 0 phase diagram is controlled by the parameter
; the critical value
and the critical temperature
at zero magnetic frustration are estimated.
The text was submitted by the authors in English. 相似文献
15.
M. Janek V. P. Ladygin L. S. Azhgirey T. Uesaka Yu. V. Gurchin M. Hatano K. Itoh A. Yu. Isupov J. -T. Karachuk H. Kato T. Kawabata V. A. Krasnov A. N. Khrenov A. S. Kiselev V. A. Kizka J. Kliman A. K. Kurilkin P. K. Kurilkin N. B. Ladygina A. N. Livanov Y. Maeda A. I. Malakhov V. Matousek M. Morhach J. Nishikawa Yu. K. Pilipenko T. Ohnishi H. Okamura S. M. Piyadin S. G. Reznikov T. Saito S. Sakaguchi H. Sakai N. Sakamoto S. Sakoda Y. Sasamoto Y. Satou K. Sekiguchi K. Suda M. A. Shikhalev A. Tamii I. Turzo N. Uchigashima T. A. Vasiliev K. Yako L. S. Zolin 《Physics of Atomic Nuclei》2008,71(9):1495-1501
The investigation of the spin structure of d, 3H, and 3He has been performed at the RIKEN acceleration research facility and VBLHE. Vector A
y
and tensor A
yy
, A
xx
, A
xz
analyzing powers for
d → 3Hen and
d → 3Hp are presented at 270 MeV. Themirror channels (3Hen and 3Hp) are comparedto each other in order to find possible manifestation of charge-symmetry breaking. The preliminary results on
the polarization observables for
d → 3Hp at 200MeV are also presented. The obtained data are compared with one-nucleon-exchange calculations.As a byproduct,
d → pX and
12C → pX breakup reactions are investigated at 140, 200, and 270MeV. The experimental data on
p elastic scattering were obtained at 270, 880, and 2000 MeV at the Nuclotron. The polarization of the deuteron beam was measured
at 270 MeV at the internal target station. The preliminary data on the vector A
y
and tensor A
yy
, A
xx
analyzing powers for the
p elastic scattering at 880 MeV are presented. The calculations on A
y
, A
yy
, and A
xx
analyzing powers for the
p elastic scattering at 880 MeV were performed in the framework of the multiple-scattering model.
The text was submitted by the authors in English. 相似文献
16.
Yisong Yang 《Communications in Mathematical Physics》1997,186(1):199-218
We study ther xr system of nonlinear elliptic equations
,a=1,2,...,r,x∈R
2, where λ τ 0 is a constant parameter,K = (Kab) is the Cartan matrix of a semi-simple Lie algebra, and βp is the Dirac measure concentrated atp
R
2. This system of equations arises in the relativistic non-Abelian Chern-Simons theory and may be viewed as a nonintegrable
deformation of the integrable Toda system. We establish the existence of a class of solutions known as topological multivortices.
The crucial step in our method is the use of the decomposition theorem of Cholesky for positive definite matrices so that
a variational principle can be formulated.
Research supported in part by the National Science Foundation under grant DMS-9596041 相似文献
17.
V. A. Bednyakov Ju. A. Budagov A. V. Gladyshev D. I. Kazakov E. V. Khramov D. I. Khubua 《Physics of Atomic Nuclei》2009,72(4):619-637
Prospects for observation of a SUSY-like signal from two gluinos are investigated within a certain region of the mSUGRA parameter space, where the cross section of the two-gluino production
in pp-collisions at the LHC ( = 14 TeV) is estimated at a rather high level of 17.3 pb. In this so-called EGRET-preferred region, the lightest stable neutralinos
χ
10 can serve as cold-dark-matter particles and can naturally explain the excess of diffuse Galactic gamma rays observed by the
EGRET space apparatus. The -event selection relies on a clear signature when decay products of each gluino contain one b
pair, one or two l
pair(s) or one or two light q
pair(s), and a neutralino. Rather high transverse missing energy carried away by the two neutralinos is the essential signature
of the events using of which allows the relevant Standard Model background to be reduced significantly. Furthermore, distributions
of the reconstructed invariant masses of two opposite-charged-lepton or light-jet pairs produced by the χ
20 → χ
10
l
+
l
− and χ
20 → χ
10
q
three-body decays have kinematic end points which measure the difference between masses of χ
20 and χ
10. In particular, it was found that these signatures of selected processes demonstrate good prospects for discovery of gluinos
at the LHC. These signatures allow one to distinguish different mSUGRA parameters m
1/2 within the EGRET-preferred region (at a higher than 6σ confidence level with 300 fb−1 data).
The text was submitted by the authors in English. 相似文献
18.
S. M. Bilenky 《Physics of Particles and Nuclei》2008,39(5):641-673
Phenomenological issues of CP violation in the quark sector of the Standard Model are discussed. We consider quark mixing in the SM, standard, and Wolfenstein
parametrization of the CKM mixing matrix and unitarity triangle. We discuss the phenomenology of CP violation in K
L
0 and B
d
0()-decays. The standard unitarity triangle fit of the existing data is discussed. In appendix A we compare the K
0 ⇆ , B
d,s
0 ⇆
, etc. oscillations with neutrino oscillations. In Appendix B we derive the evolution equation for the M − system in the Weisskopf-Wigner approximation.
The text was submitted by the author in English. 相似文献
19.
Covariant differential calculi on the quantum space
for the quantum group SL
q
(2) are classified. Our main assumptions are thatq is not a root of unity and that the differentials de
j
of the generators of
form a free right module basis for the first-order forms. Our result says, in particular, that apart from the two casesc =c(3), there exists a unique differential calculus with the above properties on the space
which corresponds to Podles' quantum sphereS
qc
/2
. 相似文献
20.
A. S. Kiselev V. P. Ladygin T. Uesaka T. A. Vasiliev M. Janek T. Saito M. Hatano A. Yu. Isupov H. Kato N. B. Ladygina Y. Maeda A. I. Malakhov J. Nishikawa T. Ohnishi H. Okamura S. G. Reznikov H. Sakai N. Sakamoto S. Sakoda Y. Satou K. Sekiguchi K. Suda A. Tamii N. Uchigashima K. Yako 《The European physical journal. Special topics》2008,162(1):143-146
The preliminary results on the tensor T20 analyzing power for the 12C(,p)13C* reaction with the excitation of 13C levels and the d(,p)X reaction at the energies T
d
= 140, 200 and 270 MeV at the emission angle Θ
cm = 0° are presented. The data on the tensor A
yy
and vector A
y
analyzing powers for the 12C(,p)13C* reaction at the energy T
d
= 270 MeV in the angular range from 4° to 18° in the laboratory are also obtained. 相似文献