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1.
Sol Schwartzman 《Communications in Mathematical Physics》2011,306(1):187-191
In n-dimensional Euclidean space let us be given an infinitely differentiable real valued function V that is bounded below. We associate with the formal operator that sends a complex valued function ψ into −div(grad ψ) + V
ψ a uniquely defined self adjoint operator which we will denote by −Δ + V. 相似文献
2.
Andrea Ferrario Carlo Antonio Rossi Thomas Willwacher 《Letters in Mathematical Physics》2011,95(1):27-39
The aim of this short note is to present a proof of the existence of an A
∞-quasi-isomorphism between the A
∞-S(V
*)-ù(V){\wedge(V)} -bimodule K, introduced in Calaque et al. (Bimodules and branes in deformation quantization, 2009), and the Koszul complex K(V) of S(V
*), viewed as an A
∞-S(V
*)-ù(V){\wedge(V)} -bimodule, for V a finite-dimensional (complex or real) vector space. 相似文献
3.
Haisheng Li 《Communications in Mathematical Physics》2005,259(2):391-411
To every vertex algebra V we associate a canonical decreasing sequence of subspaces and prove that the associated graded vector space gr(V) is naturally a vertex Poisson algebra, in particular a commutative vertex algebra. We establish a relation between this decreasing sequence and the sequence Cn introduced by Zhu. By using the (classical) algebra gr(V), we prove that for any vertex algebra V, C2-cofiniteness implies Cn-cofiniteness for all n≥2. We further use gr(V) to study generating subspaces of certain types for lower truncated ℤ-graded vertex algebras.Partially supported by an NSA grant 相似文献
4.
Series of exactly solvable non-trivial complex potentials (possessing real spectra) are generated by applying the Darboux transformation to the excited eigenstates of a non-Hermitian potential V(x). This method yields an infinite number of non-trivial partner potentials, defined over the whole real line, whose spectra are nearly exactly identical to the original potential. 相似文献
5.
Raphael Høegh-Krohn 《Communications in Mathematical Physics》1969,14(3):171-184
We consider a boson field (x) under an interaction of the form
V((x))dx, whereV() is a bounded continuous real function of a real variable . IfV() has a uniformly continuous and bounded first derivative, we prove that the Heisenberg picture field exists as weak limits of the Heisenberg picture fields corresponding to the cut-off interaction. 相似文献
6.
J. Bourgain 《Communications in Mathematical Physics》1999,204(1):207-247
In this paper, we consider the following problem. Let iu
t
+Δu+V(x,t)u= 0 be a linear Schr?dinger equation ( periodic boundary conditions) where V is a real, bounded, real analytic potential which is periodic in x and quasi periodic in t with diophantine frequency vector λ. Denote S(t) the corresponding flow map. Thus S(t) preserves the L
2-norm and our aim is to study its behaviour on H
s
(T
D
), s> 0. Our main result is the growth in time is at most logarithmic; thus if φ∈H
s
, then
More precisely, (*) is proven in 1D and 2D when V is small. We also exhibit examples showing that a growth of higher Sobolev norms may occur in this context and (*) is thus
essentially best possible.
Received: 16 October 1997 / Accepted: 28 January 1999 相似文献
7.
We apply the Asymptotic Iteration Method to obtain the bound-state energy spectrum for the d-dimensional Klein-Gordon equation with scalar S(r) and vector potentials V(r). When S(r) and V(r) are both Coulombic, we obtain all the exact solutions; when the potentials are both of Kratzer type, we obtain all the exact
solutions for S(r) = V(r); if S(r) > V(r) we obtain exact solutions under certain constraints on the potential parameters: in this case, a possible general solution
is found in terms of a monic polynomial, whose coefficients form a set of elementary symmetric polynomials.
相似文献
8.
Tina Novak 《Journal of Nonlinear Mathematical Physics》2016,23(1):74-91
In the paper, we study real forms of the complex generic Neumann system. We prove that the real forms are completely integrable Hamiltonian systems. The complex Neumann system is an example of the more general Mumford system. The Mumford system is characterized by the Lax pair (L?(λ), M?(λ)) of 2 × 2 matrices, where and U?(λ), V?(λ), W?(λ) are suitable polynomials. The topology of a regular level set of the moment map of a real form is determined by the positions of the roots of the suitable real form of U?(λ), with respect to the position of the values of suitable parameters of the system. For two families of the real forms of the complex Neumann system, we describe the topology of the regular level set of the moment map. For one of these two families the level sets are noncompact.In the paper, we also give the formula which provides the relation between two systems of the ?rst integrals in involution of the Neumann system. One of these systems is obtained from the Lax pair of the Mumford type, while the second is obtained from the Lax pair whose matrices are of dimension (n+1) × (n+1). 相似文献
9.
Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel'd [Dr], [Gr]. We exhibit in this article
an example of quadratic Poisson structure which does not arise this way.
Received: 31 May 2001 / Accepted: 17 August 2001 相似文献
10.
The scalar wave equation between the inner and the outer horizon in the Schwarzschild–de Sitter geometry is solved numerically, and the spatial variations of the field amplitude, as well as of the potential, are shown graphically. By generalizing the "tortoise" coordinate x known from Schwarzschild theory to the SdS system we first transfer the wave equation to a convenient form in which the potential V is written as a function of x. We then show how a useful "tangent" approximation can be introduced which leads to a simple, analytically invertible, relation between x and the radius r. We concentrate on two limiting cases. The first case is when the two horizons are close to each other, the so-called Nariai black hole, and the second case is when the horizons are far apart. Reflection and transmission coefficients are worked out on the basis of a replacement of the real barrier V(x) by a square barrier. 相似文献
11.
Bong H. Lian 《Communications in Mathematical Physics》1994,163(2):307-357
Inspired by a recent work of Frenkel-Zhu, we study a class of (pre-)vertex operator algebras (voa) associated to the self-dual Lie algebras. Based on a few elementary structural results we propose thatV, the category of Z+-graded prevoasV in whichV[0] is one-dimensional, is a proper setting in which to study and classify simple objects. The categoryV is organized into what we call the minimalk
th types. We introduce a functor —which we call the Frenkel-Lepowsky-Meurman functor—that attaches to each object inV a Lie algebra. This is a key idea which leads us to a (relative) classification of thesimple minimal first type. We then study the set of all Virasoro structures on a fixed minimal first typeV, and show that they are in turn classified by the orbits of the automorphism group Aut((V)) in cent((V)). Many new examples of voas are given. Finally, we introduce a generalized Kac-Casimir operator and give a simple proof of the irreducibility of the prolongation modules over the affine Lie algebras. 相似文献
12.
Yong -Cong Chen 《Journal of statistical physics》1991,65(3-4):761-771
Using a previously derived general formalism for a dissipative quantum particle in a boson bath, we prove that when the damping is Ohmic, the Kubo-Einstein relation between the diffusion constant and the linear mobilityD=kTM holds to all orders in V0 for a periodic potentialV(x)=V
0 cos(k)0
x). 相似文献
13.
It is a fundamental problem to understand why solids form crystals at zero temperature and how atomic interaction determines
the particular crystal structure that a material selects. In this paper we focus on the zero temperature case and consider
a class of atomic potentials V = V
2 + V
3, where V
2 is a pair potential of Lennard-Jones type and V
3 is a three-body potential of Stillinger-Weber type. For this class of potentials we prove that the ground state energy per
particle converges to a finite value as the number of particles tends to infinity. This value is given by the corresponding
value for a optimal hexagonal lattice, optimized with respect to the lattice spacing. Furthermore, under suitable periodic
or Dirichlet boundary condition, we show that the minimizers do form a hexagonal lattice.
Dedicated with admiration to Professor Tom Spencer on occasion of his 60th birthday 相似文献
14.
《Journal of Nonlinear Mathematical Physics》2013,20(1):31-37
Abstract Let M be an n-dimensional manifold, V the space of a representation ρ : GL(n) → GL(V). Locally, let T (V ) be the space of sections of the tensor bundle with fiber V over a sufficiently small open set U ? M, in other words, T (V ) is the space of tensor fields of type V on M on which the group Diff(M) of diffeomorphisms of M naturally acts. Elsewhere, the author classified the Diff(M)-invariant differential operators D : T (V 1) ? T (V 2) → T (V 3) for irreducible fibers with lowest weight. Here the result is generalized to bilinear operators invariant with respect to the group Diffω(M) of symplectomorphisms of the symplectic manifold (M, ω). We classify all first order invariant operators; the list of other operators is conjectural. Among the new operators we mention a 2nd order one which determins an “algebra” structure on the space of metrics (symmetric forms) on M. 相似文献
15.
Raphael Høegh-Krohn 《Communications in Mathematical Physics》1971,21(3):244-255
We consider a selfinteracting boson field in two space-time dimensions, with interaction densities of the form:V((x)): where (x) is a scalar boson field, andV() is a real positive function of exponential type. We define the space cut-off interaction by
and prove thatH
r
=H
0+V
r
, whereH
0 is the free energy, is essentially self adjoint. This permits us to take away the space cut-off and we obtain a quantum field free of cut-offs.At leave from Mathematical Institute, Oslo University.This research partially sponsored by the Air Force Office of Scientific Research under Contract AF 49(638)1545. 相似文献
16.
We establish some properties of quantum quasi-shuffle algebras. They include the necessary and sufficient condition for the
construction of the quantum quasi-shuffle product, the universal property, and the commutativity condition. As an application,
we use the quantum quasi-shuffle product to construct a linear basis of T(V), for a special kind of Yang–Baxter algebras (V, m, σ). 相似文献
17.
Raziye Ertuğrul 《辐射效应与固体损伤》2013,168(9):791-799
The effects of gamma irradiation on electrical parameters of Au/Si3N4/n-Si (MIS) structure were investigated by using the capacitance–voltage (C–V) and conductance–voltage (G/ω–V) measurements. The MIS structure was irradiated using gamma-radiation source at a dose rate of 0.69?kGy/h. The C–V and G/ω–V measurements were carried out at a total dose range of 0–100?kGy for five different frequencies (1, 10, 100, 500 and 1000?kHz). The obtained results showed that the C and G/ω values decrease with the increasing radiation dose due to the irradiation-induced defects at the interface. Also, the observed decrease in the C and G/ω values with the increasing frequency was explained on the basis of interface states (Nss). The values of series resistance (Rs) increase with the increasing radiation dose. To obtain the real capacitance and conductance of the capacitor, the measured values of C and G/ω were corrected to eliminate the effect of series resistance. The values of Nss were determined by using the conductance method and were decreased with the increasing radiation dose. 相似文献
18.
Katrina Barron Chongying Dong Geoffrey Mason 《Communications in Mathematical Physics》2002,227(2):349-384
Let V be a vertex operator algebra, and for k a positive integer, let g be a k-cycle permutation of the vertex operator algebra V
⊗
k
. We prove that the categories of weak, weak admissible and ordinary g-twisted modules for the tensor product vertex operator algebra V
⊗
k
are isomorphic to the categories of weak, weak admissible and ordinary V-modules, respectively. The main result is an explicit construction of the weak g-twisted V
⊗
k
-modules from weak V-modules. For an arbitrary permutation automorphism g of V
⊗
k
the category of weak admissible g-twisted modules for V
⊗
k
is semisimple and the simple objects are determined if V is rational. In addition, we extend these results to the more general setting of γg-twisted V
⊗
k
-modules for γ a general automorphism of V acting diagonally on V
⊗
k
and g a permutation automorphism of V
⊗
k
.
Received: 20 April 2000 / Accepted: 20 January 2002 相似文献
19.
Deokki Min Nils Hoivik Geir Uri Jensen Frode Tyholdt Camilla Haavik Ulrik Hanke 《Applied Physics A: Materials Science & Processing》2011,105(4):867-874
The dielectric properties of zirconium dioxide (ZrO2) ceramic thin films were characterized up to 50 GHz using coplanar waveguides (CPWs) and metal–insulator–metal (MIM) capacitors
with top circular electrodes. The ZrO2 films were deposited using a chemical solution onto high-resistivity Si wafers and metal layers. The real part of the dielectric
constant of approximately 22 and 26 was extracted at 50 GHz for CPW and MIM structures, respectively, and the loss tangent
was approximately 0.09 at 50 GHz. C–V and I–V measurements were carried out to determine low-frequency and DC dielectric properties. The measurement results indicate that
ZrO2 is a promising material to be used as a dielectric layer for radio-frequency (RF) microelectromechanical systems (MEMS) capacitive
switches. 相似文献
20.
We consider the time evolution of a disk under the action of a constant force and interacting with a free gas in the mean-field
approximation. Letting V0>0 be the initial velocity of the disk and V∞>0 its equilibrium velocity, namely the one for which the external field is balanced by the friction force exerted by the
background, we show that, if V∞−V0 is positive and sufficiently small, then the disk reaches V∞ with the power law t−(d+2), d=1,2,3 being the dimension of the physical space. The reason for this behavior is the long tail memory due to recollisions.
Any Markovian approximation (or simply neglecting the recollisions) yields an exponential approach to equilibrium. 相似文献