共查询到20条相似文献,搜索用时 31 毫秒
1.
V. R. Khalilov 《Theoretical and Mathematical Physics》2013,175(2):637-654
We consider the motion of a relativistic charged zero-mass fermion in Coulomb and Aharonov-Bohm potentials in 2+1 dimensions. With these singular external potentials, we construct one-parameter self-adjoint Dirac Hamiltonians classified by self-adjoint boundary conditions. We show that if the so-called effective charge becomes overcritical, then virtual (quasistationary) bound states occur. The wave functions corresponding to these states have large amplitudes near the Coulomb center, and their energy spectrum is quasidiscrete and consists of a number of broadened levels of a width related to the inverse lifetime of the quasistationary state. We derive equations for the quasidiscrete spectra and quasistationary state lifetimes and solve these equations in physically interesting cases. We study the so-called local densities of state, which can be assessed in physical experiments, as functions of the energy and the problem parameters, investigating these densities both analytically and graphically. 相似文献
2.
We consider the problem of two bodies with a central interaction on simply connected constant-curvature spaces of arbitrary
dimension. We construct the self-adjoint extension of the quantum Hamiltonian, which was explicitly expressed through the
radial differential operator and the generators of the isometry group of a configuration space in Part I of this paper. Exact
spectral series are constructed for several potentials in the space
.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 3, pp. 481–489, September, 2000. 相似文献
3.
O. Yu. Shvedov 《Theoretical and Mathematical Physics》2000,125(1):1377-1390
We consider an exactly solvable quantum mechanical model with an infinite number of degrees of freedom that is an analogue
of the model of N scalar fields (λ/N)(ϕa
a)2 in the leading order in 1/N. The model involves vacuum and S-matrix divergences and also the Stückelberg divergences, which
are absent in other known renormalizable quantum mechanical models with, divergences (such as the particle in a δ-shape potential
or the Lee model). To eliminate divergences, we renormalize the vacuum energy and charge and transform the Hamiltonian by
a unitary transformation with a singular dependence on the regularization parameter. We construct the Hilbert space with a
positive-definite metric, a self-adjoint Hamiltonian operator, and a representation for the operators of physical quantities.
Neglecting the terms that lead to the vacuum divergences fails to improve and, on the contrary, worsens the renormalizability
properties of the model.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 1, pp. 91–106, October, 2000. 相似文献
4.
A. M. Semikhatov 《Theoretical and Mathematical Physics》2007,153(3):1597-1642
For positive integers p = k + 2, we construct a logarithmic extension of the
conformal field theory of integrable representations by taking the kernel of two fermionic screening operators in a butterfly
resolution of a three-boson realization of
. The currents W−(z) and W+(z) of a W-algebra acting in the kernel are determined by a highest-weight state of dimension 4p − 2 and charge 2p − 1 and
by a (θ=1)-twisted highest-weight state of the same dimension 4p − 2 and opposite charge −2p+1. We construct 2p W-algebra
representations, evaluate their characters, and show that together with the p−1 integrable representation characters, they
generate a modular group representation whose structure is described as a deformation of the (9p−3)-dimensional representation
R
p+1⊕ℂ2⊗R
p+1ʕR
p−1⊕ℂ2
R
p−1⊕ℂ3
R
p−1, where R
p−1 is the SL(2, ℤ)-representation on
integrable-representation characters and R
p+1 is a (p+1)-dimensional SL(2, ℤ)-representation known from the logarithmic (p, 1) model. The dimension 9p − 3 is conjecturally
the dimension of the space of torus amplitudes, and the ℂn with n = 2 and 3 suggest the Jordan cell sizes in indecomposable W-algebra modules. We show that under Hamiltonian reduction,
the W-algebra currents map into the currents of the triplet W-algebra of the logarithmic (p, 1) model.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 291–346, December, 2007. 相似文献
5.
B. L. Voronov D. M. Gitman A. D. Levin R. Ferreira 《Theoretical and Mathematical Physics》2016,187(2):633-648
We consider the peculiarities of the electron energy spectrum in the Coulomb field of a superheavy nucleus and discuss the long history of an incorrect interpretation of this problem in the case of a pointlike nucleus and its current correct solution. We consider the spectral problem in the case of a regularized Coulomb potential. For some special regularizations, we derive an exact equation for the point spectrum in the energy interval (-m,m) and find some of its solutions numerically. We also derive an exact equation for charges yielding bound states with the energy E = -m; some call them supercritical charges. We show the existence of an infinite number of such charges. Their existence does not mean that the oneparticle relativistic quantum mechanics based on the Dirac Hamiltonian with the Coulomb field of such charges is mathematically inconsistent, although it is physically unacceptable because the spectrum of the Hamiltonian is unbounded from below. The question of constructing a consistent nonperturbative second-quantized theory remains open, and the consequences of the existence of supercritical charges from the standpoint of the possibility of constructing such a theory also remain unclear. 相似文献
6.
Cheng Jun Hou 《数学学报(英文版)》2008,24(6):983-996
We introduce two notions of the pressure in operator algebras, one is the pressure Pα(π, T) for an automorphism α of a unital exact C^*-algebra A at a self-adjoint element T in A with respect to a faithful unital *-representation π the other is the pressure Pτ,α(T) for an automorphism α of a hyperfinite von Neumann algebra M at a self-adjoint element T in M with respect to a faithful normal α-invariant state τ. We give some properties of the pressure, show that it is a conjugate invaxiant, and also prove that the pressure of the implementing inner automorphism of a crossed product A×α Z at a self-adjoint operator T in A equals that of α at T. 相似文献
7.
M. P. Kharlamov 《Regular and Chaotic Dynamics》2007,12(3):267-280
We consider an analogue of the 4th Appelrot class of motions of the Kowalevski top for the case of two constant force fields.
The trajectories of this family fill a four-dimensional surface
in the six-dimensional phase space. The constants of the three first integrals in involution restricted to this surface fill
one of the sheets of the bifurcation diagram in ℝ3. We point out a pair of partial integrals to obtain explicit parametric equations of this sheet. The induced system on
is shown to be Hamiltonian with two degrees of freedom having a thin set of points where the induced symplectic structure
degenerates. The region of existence of motions in terms of the integral constants is found. We provide the separation of
variables on
and algebraic formulae for the initial phase variables.
相似文献
8.
From Repeated to Continuous Quantum Interactions 总被引:5,自引:0,他引:5
9.
We consider the Allen–Cahn equation
where Ω is a smooth and bounded domain in
such that the mean curvature is positive at each boundary point. We show that there exists a sequence ε j → 0 such that the Allen–Cahn equation has a solution
with an interface which approaches the boundary as j → + ∞. 相似文献
10.
V. R. Khalilov 《Theoretical and Mathematical Physics》1998,116(2):956-963
The creation of charged fermion pairs by a strong external Coulomb field in a space with two dimensions is investigated. Exact
solutions to the Dirac equation are found for the Coulomb external field in 2+1 dimensions. The equation for determining the
critical charge is obtained and is numerically solved for a simplified model. The critical charge for 2+1 dimensions is much
less than the critical charge for the similar model with 3+1 dimensions. The influence of the vacuum polarization on the critical
charge is studied in the one-loop approximation to the (2+1)-dimensional quantum electrodynamics.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 116, No. 2, pp. 277–287, August, 1998. 相似文献
11.
A. L. Smirnov 《Journal of Mathematical Sciences》2008,151(3):3052-3068
12.
Thomas Strömberg 《Journal of Evolution Equations》2007,7(4):669-700
Let H (t, x, p) be a Hamiltonian function that is convex in p. Let the associated Lagrangian satisfy the nonstandard minorization condition
where m > 0, ω > 0, and C ≥ 0 are constants. Under some additional conditions, we prove that the associated value function is the unique viscosity
solution of S
t
+ H(t, x, ∇S) = 0 in , without any conditions at infinity on the solution. Here ωT < π/2. To the Hamilton–Jacobi equation corresponding to the classical action integrand in mechanics, we adjoin the continuity
equation and establish the existence and uniqueness of a viscosity–measure solution (S, ρ) of
This system arises in the WKB method. The measure solution is defined by means of the Filippov flow of ∇S.
相似文献
13.
Jingbo Xia 《Transactions of the American Mathematical Society》1999,351(5):1989-2023
We study the self-adjoint extensions of the Dirac operator , where the electrical potential contains a Coulomb singularity of arbitrary charge and the magnetic potential is allowed to be unbounded at infinity. We show that if the Coulomb singularity has the form where has a limit at 0, then, for any self-adjoint extension of the Dirac operator, removing the singularity results in a Hilbert-Schmidt perturbation of its resolvent.
14.
A. V. Kotikov L. N. Lipatov A. I. Onishchenko V. N. Velizhanin 《Theoretical and Mathematical Physics》2007,150(2):213-224
We present results for the universal anomalous dimension γun(j) of Wilson twist-2 operators in the
supersymmetric Yang-Mills theory in the first three orders of the perturbation theory. We obtain these expressions by extracting
the most complicated terms from the corresponding anomalous dimensions in QCD. The result obtained agrees with the hypothesis
of the integrability of the
supersymmetric Yang-Mills theory in the context of the AdS/CFT correspondence.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 2, pp. 249–262, February, 2007. 相似文献
15.
Selfdual variational principles are introduced in order to construct solutions for Hamiltonian and other dynamical systems which satisfy a variety of linear and nonlinear boundary conditions including many of the standard ones. These principles lead to new variational proofs of the existence of parabolic flows with prescribed initial conditions, as well as periodic, anti-periodic and skew-periodic orbits of Hamiltonian systems. They are based on the theory of anti-selfdual Lagrangians developed recently in Ghoussoub (2007a b c). 相似文献
16.
M. Przybylska 《Regular and Chaotic Dynamics》2009,14(2):263-311
We consider natural complex Hamiltonian systems with n degrees of freedom given by a Hamiltonian function which is a sum of the standard kinetic energy and a homogeneous polynomial
potential V of degree k > 2. The well known Morales-Ramis theorem gives the strongest known necessary conditions for the Liouville integrability
of such systems. It states that for each k there exists an explicitly known infinite set ⊂ ℚ such that if the system is integrable, then all eigenvalues of the Hessian matrix V″(d) calculated at a non-zero d ∈ ℂ
n
satisfying V′(d) = d, belong to .
The aim of this paper is, among others, to sharpen this result. Under certain genericity assumption concerning V we prove the following fact. For each k and n there exists a finite set such that if the system is integrable, then all eigenvalues of the Hessian matrix V″(d) belong to . We give an algorithm which allows to find sets .
We applied this results for the case n = k = 3 and we found all integrable potentials satisfying the genericity assumption. Among them several are new and they are
integrable in a highly non-trivial way. We found three potentials for which the additional first integrals are of degree 4
and 6 with respect to the momenta.
相似文献
17.
A. B. Aleksandrov 《Journal of Mathematical Sciences》2000,101(3):3049-3052
We present an example of a set {
} satisfying the following two conditions: (1) there exists a nonzero positive singular measure on the unit circle {
} with spectrum in Λ; (2) if the spectrum of f∈L1 {
} is contained in Λ and f vanishes on a set of positive measure, then f=0. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 7–14.
Translated by A. B. Aleksandrov. 相似文献
18.
Yin Qun Liu DeqingDept.of Appl.Math. Nanjing Univ.of Science Technology Nanjing 《高校应用数学学报(英文版)》2000,15(3):259-266
§1 IntroductionInthispaperwediscusstheexistenceofthesolutionforthefollowingsecondorderHamiltoniansystemx¨ Ax ΔF(x)=0,(1.1)whereAisann×nrealsymmetricmatrixandisnon-definite,F∈C1(Rn,R),andΔF(x)denotesthegradientofF.WhileworksforsecondorderHamiltonsystemshavemostlybeendoneundertheconditionA=0,westudythecasewhereA≠0andisnon-definiteinthepapers[1,2].DefineH=H1,2T([0,T],Rn)={x:R→Rn|xisabsolutelycontinuous,x∈L2([0,T],Rn),x(0)=x(T),x(0)=x(T)}and〈x,y〉=∫T0[(x(t),y(t)) (x… 相似文献
19.
With a quantum Markov semigroup (Τ
t
)
t≥0 on
, whichhas a faithful normal invariant state ρ, we associate semigroupsT
(s)
(s∈[0],[1]) on the set of Hilbert-Schmidt operators onh defined by the rule
. This allows us to use spectral theory to study the infinitesimal generatorL
(s)
of the semigroupT
(s)
and deduce information on the rate of the decay to equilibrium of Τ by means of estimates of the spectral gap ofL
(s)
. Fors=1/2, this method is applied to a class of quantum Markov semigroups on
. We prove simple but reasonably general sufficient conditions, as well as necessary and sufficient conditions, for the gap(L
(1/2)) to be positive. The exact value of the gap(L
(1/2)) is computed or estimated for a certain class of equations motivated by classical probability or physical applications.
Translated fromMatematicheskie Zametki, Vol. 68, No. 4, pp. 523–538, October, 2000. 相似文献
20.
Annunziata Loiudice 《manuscripta mathematica》2007,124(2):247-259
We prove existence and multiplicity of solutions for the semilinear subelliptic problem with critical growth in Ω, u = 0 on ∂Ω, where is a sublaplacian on a Carnot group , 2* = 2Q/(Q − 2) is the critical Sobolev exponent for and Ω is a bounded domain of . 相似文献