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1.
Emanuela Caliceti 《Czechoslovak Journal of Physics》2005,55(9):1077-1080
Some recent results are described on the reality of the spectrum of
-symmetric Schrodinger operators, obtained by perturbing a class of quantum nonlinear oscillators by means of suitable relatively
bounded perturbations.
Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22,
2005. 相似文献
2.
H. Bila V. Jakubsky M. Znojil B. Bagchi S. Mallik C. Quesne 《Czechoslovak Journal of Physics》2005,55(9):1075-1076
Inside a box of size L we contemplate the simplest
-symmetric piece-wise constant potential of size ℓ < L and purely imaginary strength ig and describe all its bound states in closed form.
Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22,
2005. 相似文献
3.
Finitely generated free modular ortholattices. II 总被引:2,自引:0,他引:2
M. Haviar P. Konôpka C. B. Wegener 《International Journal of Theoretical Physics》1997,36(12):2661-2679
4.
Ersan Demiralp 《Czechoslovak Journal of Physics》2005,55(9):1081-1084
We have investigated bound state solutions of the Schrodinger equation for one-dimensional harmonic oscillator potential together
with even number of Dirac delta functions. These point interactions are located at symmetric points x = x
i
and x = −x
i
(i = 1, 2,..., N) and they have complex conjugate strengths
and
, respectively. We present explicit forms of eigenfunctions and an algebraic eigenvalue equation and numerical solutions for
this
-symmetric Hamiltonian.
Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22,
2005. 相似文献
5.
N. M. Panyunin 《Russian Journal of Mathematical Physics》2008,15(4):511-521
In the paper, evolution pseudodifferential equations in the space of superanalytic functions (X) of an infinite-dimensional argument with symbols in the space (Y) of Fourier supertransforms of distributions on the dual superspace are considered. For these equations, the “weak” Cauchy
problem is posed and the existence theorem for the solutions of this problem is proved. The main result of the paper is the
theorem concerning the representation of solutions of the “weak” Cauchy problem by the Feynman path integral in the phase
superspace (the Feynman-Kac formula). The Feynman integral is understood in the sequential sense. Thus, the Feynman formula
becomes an immediate consequence of the Feynman-Kac formula. 相似文献
6.
A semi-phenomenological theory of variable-range hopping (VRH) is developed for two-dimensional (2D) quasi-one-dimensional
(quasi-1D) systems such as arrays of quantum wires in the Wigner crystal regime. The theory follows the phenomenology of Efros,
Mott and Shklovskii allied with microscopic arguments. We first derive the Coulomb gap in the single-particle density of states,
g(ε), where ε is the energy of the charge excitation. We then derive the main exponential dependence of the electron conductivity
in the linear (L), i.e. σ(T) ∼exp [-(TL/T)γL], and current in the non-linear (NL), i.e.
, response regimes (
is the applied electric field). Due to the strong anisotropy of the system and its peculiar dielectric properties we show
that unusual, with respect to known results, Coulomb gaps open followed by unusual VRH laws, i.e. with respect to the disorder-dependence
of TL and
and the values of γL and γNL. 相似文献
7.
The conformal anomaly and a contribution to the one-loop effective action associated with the product
of the Laplace operators
, p=1,2 acting in irreducible rank 1 symmetric spaces are calculated. The explicit form of the zeta functions and the conformal
anomaly of the stress-energy momentum tensor is derived.
Pis’ma Zh. éksp. Teor. Fiz. 67, No. 3, 166–171 (10 February 1998)
Published in English in the original Russian journal. Edited by Steve Torstveit. 相似文献
8.
The spectra of self-adjoint operators in Krein spaces are known to possess real sectors as well as sectors of pair-wise complex
conjugate eigenvalues. Transitions from one spectral sector to the other are a rather generic feature and they usually occur
at exceptional points of square root branching type. For certain parameter configurations two or more such exceptional points
may happen to coalesce and to form a higher-order branch point. We study the coalescence of two square root branch points
semi-analytically for a
-symmetric 4 × 4 matrix toy model and illustrate its occurrence numerically in the spectrum of the 2 × 2 operator matrix of
the magneto-hydrodynamic α 2-dynamo and an extended version of the hydrodynamic Squire equation.
Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22,
2005. 相似文献
9.
Given a conditionally completely positive map on a unital *-algebra , we find an interesting connection between the second Hochschild cohomology of with coefficients in the bimodule of adjointable maps, where M is the GNS bimodule of , and the possibility of constructing a quantum random walk [in the sense of (Attal et al. in Ann Henri Poincar 7(1):59–104,
2006; Lindsay and Parthasarathy in Sankhya Ser A 50(2):151–170, 1988; Sahu in Quantum stochastic Dilation of a class of Quantum
dynamical Semigroups and Quantum random walks. Indian Statistical Institute, 2005; Sinha in Banach Center Publ 73:377–390,
2006)] corresponding to .
D. Goswami was supported by a project funded by the Indian National Academy of Sciences.
L. Sahu had research support from the National Board of Higher Mathematics, DAE (India) is gratefully acknowledged. 相似文献
10.
In view of current interest in the trapping of antihydrogen (
) atoms at low temperatures [1–3], we have carried out a full four-body variational calculation to determine s-wave elastic phase shifts for hydrogen antihydrogen scattering, using the Kohn Variational Principle. Terms outside the Born–Oppenheimer
approximation have been taken into account using the formalism of Kołos and Wolniewicz [4]. As far as we are aware, this is
the first time that these terms have been included in an H
scattering calculation. This is a continuation of earlier work on H–
interactions [5–7]. Preliminary results differ substantially from those calculated using the Born–Oppenheimer approximation
[8–10]. A method is outlined for reducing this discrepancy and taking the rearrangement channel into account.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
11.
G. Lévai 《Czechoslovak Journal of Physics》2006,56(9):953-966
The Scarf I and Scarf II potentials are discussed within a common mathematical framework, which is then specified to handle
the two potentials separately both in the conventional Hermitian and in the
-symmetric setting. The physically admissible solutions are identified in each case together with the corresponding energy
eigenvalues. Several main differences between the
-symmetric Scarf I and II potentials are pointed out. These include the presence and absence of the quasi-parity quantum number,
the sign of the pseudo-norm, the mechanism of the spontaneous breakdown of
symmetry and the non-
orthogonality of otherwise admissible solutions in the Scarf I potential. Similarities and differences with respect to the
corresponding Hermitian systems are also pointed out. 相似文献
12.
In their 1936 founding paper on quantum logic, Birkhoff and von Neumann postulated that the lattice describing the experimental
propositions concerning a quantum system is orthocomplemented. We prove that this postulate fails for the lattice
sep describing a compound system consisting of so called separated quantum systems. By separated we mean two systems prepared in different “rooms” of the lab, and before any interaction takes
place. In that case, the state of the compound system is necessarily a product state. As a consequence, Dirac’s superposition
principle fails, and therefore
sep cannot satisfy all Piron’s axioms. In previous works, assuming that
sep is orthocomplemented, it was argued that
sep is not orthomodular and fails to have the covering property. Here we prove that
sep cannot admit an orthocomplementation. Moreover, we propose a natural model for
sep which has the covering property.
PACS: 03.65.Ta, 03.65.Ca 相似文献
13.
Carl M. Bender 《Czechoslovak Journal of Physics》2005,55(9):1067-1074
The Lee model is an elementary quantum field theory in which mass, wave-function, and charge renormalization can be performed
exactly. In early studies of this model in the 1950's it was found that there is a critical value of g
2, the square of the renormalized coupling constant, above which g
0
2
, the square of the unrenormalized coupling constant, is negative. For g
2 larger than this critical value, the Hamiltonian of the Lee model becomes non-Hermitian. In this non-Hermitian regime a new
state appears whose norm is negative. This state is called a ghost. It has always been thought that in this ghost regime the Lee model is an unacceptable quantum theory because unitarity appears
to be violated. However, in this regime while the Hamiltonian is not Hermitian, it does possess
symmetry. It has recently been discovered that a non-Hermitian Hamiltonian having
symmetry may define a quantum theory that is unitary. The proof of unitarity requires the construction of a time-independent
operator called C. In terms of C one can define a new inner product with respect to which the norms of the states in the Hilbert space are positive. Furthermore,
it has been shown that time evolution in such a theory is unitary. In this talk the C operator for the Lee model in the ghost regime is constructed in the V/Nθ sector. It is then shown that the ghost state has a positive norm and that the Lee model is an acceptable unitary quantum
field theory for all values of g
2.
Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22,
2005. 相似文献
14.
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
15.
16.
We show that there are canonical isomorphisms between Hochschild cohomology spaces
, where
is the algebra of smooth functions on a manifold M and
the space of skew multivector fields over M. This implies that continuous and differential deformation theories of
coincide. 相似文献
17.
Carl M. Bender 《Czechoslovak Journal of Physics》2006,56(9):1047-1062
In this paper, two independent methods are used to show that the non-Hermitian
-symmetric wrong-sign quartic Hamiltonian H = (1/2m)p
2 − gx
4 is exactly equivalent to the conventional Hermitian Hamiltonian
. First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated
by using functional-integration methods. As the linear term in the Hermitian Hamiltonian
is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly
is a consequence of the broken parity symmetry of the original non-Hermitian
-symmetric Hamiltonian. The anomaly term in
remains unchanged if an x
2 term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in
are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states. 相似文献
18.
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
19.
G. Abbiendi et al. 《The European Physical Journal C - Particles and Fields》2006,45(2):307-335
The mass and width of the W boson are measured using e+e– → W+W– events from the data sample collected by the OPAL experiment at LEP at centre-of-mass energies between 170 GeV and 209 GeV.
The mass (mW) and width (ΓW) are determined using direct reconstruction of the kinematics of W+W– →
and W+W– →
events. When combined with previous OPAL measurements using W+W– →
events and the dependence on of the WW production cross-section at threshold, the results are determined to be
where the first error is statistical, the second systematic and the third due to uncertainties in the value of the LEP beam
energy. By measuring in the channel using several different determinations of the direction of jets with differing sensitivities
to soft particles, a limit is also obtained on possible final-state interactions due to colour reconnection effects inW+W– →
events. The consistency of the results for the W mass and width with those inferred from other electroweak parameters provides
an important test of the Standard Model of electroweak interactions.
Arrival of the final proofs: 28 November 2005
This paper is dedicated to the memory of Steve O'Neale 相似文献
20.
The $
\mathcal{P}\mathcal{T}
$
\mathcal{P}\mathcal{T}
symmetry of the Coulomb potential and its solutions are studied along trajectories satisfying the $
\mathcal{P}\mathcal{T}
$
\mathcal{P}\mathcal{T}
symmetry requirement. It is shown that with appropriate normalization constant the general solutions can be chosen $
\mathcal{P}\mathcal{T}
$
\mathcal{P}\mathcal{T}
-symmetric if the L parameter that corresponds to angular momentum in the Hermitian case is real. $
\mathcal{P}\mathcal{T}
$
\mathcal{P}\mathcal{T}
symmetry is spontaneously broken, however, for complex L values of the form L = −1/2 + iλ. In this case the potential remains $
\mathcal{P}\mathcal{T}
$
\mathcal{P}\mathcal{T}
-symmetric, while the two independent solutions are transformed to each other by the $
\mathcal{P}\mathcal{T}
$
\mathcal{P}\mathcal{T}
operation and at the same time, the two series of discrete energy eigenvalues turn into each other’s complex conjugate. 相似文献