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1.
2.
Pulak Ranjan Giri 《International Journal of Theoretical Physics》2008,47(7):2095-2100
We show that the total time of evolution from the initial quantum state to final quantum state and then back to the initial
state, i.e., making a round trip along the great circle over S
2, must have a lower bound in quantum mechanics, if the difference between two eigenstates of the 2×2 Hamiltonian is kept fixed.
Even the non-hermitian quantum mechanics can not reduce it to arbitrarily small value. In fact, we show that whether one uses
a hermitian Hamiltonian or a non-hermitian, the required minimal total time of evolution is same. It is argued that in hermitian
quantum mechanics the condition for minimal time evolution can be understood as a constraint coming from the orthogonality
of the polarization vector P of the evolving quantum state
with the vector
of the 2×2 hermitian Hamiltonians
and it is shown that the Hamiltonian H can be parameterized by two independent parameters
and Θ. 相似文献
3.
M. Diehl 《The European Physical Journal C - Particles and Fields》2003,31(2):277-277
The kinematical factor in the positivity bound (36) is incorrect. The bound correctly reads
Our corrected result agrees with inequality (25) in [1], taking into account the different normalization conventions here and there.Published online: 9 October 2003Erratum published online: 10 October 2003 相似文献
4.
Asao Arai 《Letters in Mathematical Physics》2008,85(1):15-25
Let (T, H) be a weak Weyl representation of the canonical commutation relation (CCR) with one degree of freedom. Namely T is a symmetric operator and H is a self-adjoint operator on a complex Hilbert space satisfying the weak Weyl relation: for all (the set of real numbers), e−itH
D(T) ⊂ D(T) (i is the imaginary unit and D(T) denotes the domain of T) and . In the context of quantum theory where H is a Hamiltonian, T is called a strong time operator of H. In this paper we prove the following theorem on uniqueness of weak Weyl representations: Let be separable. Assume that H is bounded below with and , where is the set of complex numbers and, for a linear operator A on a Hilbert space, σ(A) denotes the spectrum of A. Then ( is the closure of T) is unitarily equivalent to a direct sum of the weak Weyl representation on the Hilbert space , where is the multiplication operator by the variable and with . Using this theorem, we construct a Weyl representation of the CCR from the weak Weyl representation .
This work is supported by the Grant-in-Aid No.17340032 for Scientific Research from Japan Society for the Promotion of Science
(JSPS). 相似文献
5.
A new parametrization of the 3-metric allows to find explicitly a York map by means of a partial Shanmugadhasan canonical
transformation in canonical ADM tetrad gravity. This allows to identify the two pairs of physical tidal degrees of freedom
(the Dirac observables of the gravitational field have to be built in term of them) and 14 gauge variables. These gauge quantities,
whose role in describing generalized inertial effects is clarified, are all configurational except one, the York time, i.e.
the trace of the extrinsic curvature of the instantaneous 3-spaces (corresponding to a clock synchronization convention) of a non-inertial frame centered on an arbitrary observer. In the Dirac Hamiltonian is the sum of the weak ADM energy (whose density is coordinate-dependent, containing the inertial potentials) and of the first-class constraints. The main results of the
paper, deriving from a coherent use of constraint theory, are: (i) The explicit form of the Hamilton equations for the two
tidal degrees of freedom of the gravitational field in an arbitrary gauge: a deterministic evolution can be defined only in
a completely fixed gauge, i.e. in a non-inertial frame with its pattern of inertial forces. The simplest such gauge is the
3-orthogonal one, but other gauges are discussed and the Hamiltonian interpretation of the harmonic gauges is given. This
frame-dependence derives from the geometrical view of the gravitational field and is lost when the theory is reduced to a
linear spin 2 field on a background space-time. (ii) A general solution of the super-momentum constraints, which shows the
existence of a generalized Gribov ambiguity associated to the 3-diffeomorphism gauge group. It influences: (a) the explicit
form of the solution of the super-momentum constraint and then of the Dirac Hamiltonian; (b) the determination of the shift
functions and then of the lapse one. (iii) The dependence of the Hamilton equations for the two pairs of dynamical gravitational
degrees of freedom (the generalized tidal effects) and for the matter, written in a completely fixed 3-orthogonal Schwinger
time gauge, upon the gauge variable , determining the convention of clock synchronization. The associated relativistic inertial effects, absent in Newtonian
gravity and implying inertial forces changing from attractive to repulsive in regions with different sign of , are completely unexplored and may have astrophysical relevance in the interpretation of the dark side of the universe. 相似文献
6.
Jürg Fröhlich B. Lars G. Jonsson Enno Lenzmann 《Communications in Mathematical Physics》2007,274(1):1-30
We study the nonlinear equation
which is known to describe the dynamics of pseudo-relativistic boson stars in the mean-field limit. For positive mass parameters,
m > 0, we prove existence of travelling solitary waves, , for some and with speed |v| < 1, where c = 1 corresponds to the speed of light in our units. Due to the lack of Lorentz covariance, such travelling solitary waves
cannot be obtained by applying a Lorentz boost to a solitary wave at rest (with v = 0). To overcome this difficulty, we introduce and study an appropriate variational problem that yields the functions as minimizers, which we call boosted ground states. Our existence proof makes extensive use of concentration-compactness-type
arguments.
In addition to their existence, we prove orbital stability of travelling solitary waves and pointwise exponential decay of in x. 相似文献
7.
We provide a uniform decay estimate for the local energy of general solutions to the inhomogeneous wave equation on a Schwarzschild
background. Our estimate implies that such solutions have asymptotic behavior
as long as the source term is bounded in the norm
. In particular this gives scattering at small amplitudes for non-linear scalar fields of the form
for all 2 < p.
This paper is dedicated to the memory of Hope Machedon
The second author would like thank MSRI and Princeton University, where a portion of this research was conducted during the
Fall of 2005. The second author was also supported by a NSF postdoctoral fellowship. 相似文献
8.
Kunji Nakayama 《International Journal of Theoretical Physics》2008,47(7):2065-2094
This paper deals with topos-theoretic truth-value valuations of quantum propositions. Concretely, a mathematical framework
of a specific type of modal approach is extended to the topos theory, and further, structures of the obtained truth-value
valuations are investigated. What is taken up is the modal approach based on a determinate lattice
, which is a sublattice of the lattice
of all quantum propositions and is determined by a quantum state e and a preferred determinate observable R. Topos-theoretic extension is made in the functor category
of which base category
is determined by R. Each true atom, which determines truth values, true or false, of all propositions in
, generates also a multi-valued valuation function of which domain and range are
and a Heyting algebra given by the subobject classifier in
, respectively. All true propositions in
are assigned the top element of the Heyting algebra by the valuation function. False propositions including the null proposition
are, however, assigned values larger than the bottom element. This defect can be removed by use of a subobject semi-classifier.
Furthermore, in order to treat all possible determinate observables in a unified framework, another valuations are constructed
in the functor category
. Here, the base category
includes all
’s as subcategories. Although
has a structure apparently different from
, a subobject semi-classifier of
gives valuations completely equivalent to those in
’s. 相似文献
9.
V. Gaftoi J. Lopez-Bonilla G. Ovando 《International Journal of Theoretical Physics》1999,38(3):939-943
Weert found a superpotential
for the bounded part of the Maxwelltensor
associatedto the Lienard–Wiechert field. Here we obtain afourth-rank generator
for the superpotential
. 相似文献
10.
Quantum Conjugacy Classes of Simple Matrix Groups 总被引:1,自引:0,他引:1
A. Mudrov 《Communications in Mathematical Physics》2007,272(3):635-660
Let G be a simple complex classical group and its Lie algebra. Let be the Drinfeld-Jimbo quantization of the universal enveloping algebra . We construct an explicit -equivariant quantization of conjugacy classes of G with Levi subgroups as the stabilizers.
Dedicated to the memory of Joseph Donin
This research is partially supported by the Emmy Noether Research Institute for Mathematics, the Minerva Foundation of Germany,
the Excellency Center “Group Theoretic Methods in the study of Algebraic Varieties” of the Israel Science foundation, by the
EPSRC grant C511166, and by the RFBR grant no. 06-01-00451. 相似文献
11.
In this paper we have analyzed the Kaluza-Klein type Robertson Walker (RW) cosmological models by considering three different
forms of variable Λ:
,
and Λ∼ρ. It is found that, the connecting free parameters of the models with cosmic matter and vacuum energy density parameters are
equivalent, in the context of higher dimensional space time. The expression for the look back time, luminosity distance and
angular diameter distance are also derived. This work has thus generalized to higher dimensions the well-known results in
four dimensional space time. It is found that there may be significant difference in principle at least, from the analogous
situation in four dimensional space time. 相似文献
12.
Asao Arai 《Letters in Mathematical Physics》2007,80(3):211-221
Let H be a self-adjoint operator on a complex Hilbert space . A symmetric operator T on is called a time operator of H if, for all , (D(T) denotes the domain of T) and . In this paper, spectral properties of T are investigated. The following results are obtained: (i) If H is bounded below, then σ(T), the spectrum of T, is either (the set of complex numbers) or . (ii) If H is bounded above, then is either or . (iii) If H is bounded, then . The spectrum of time operators of free Hamiltonians for both nonrelativistic and relativistic particles is exactly identified.
Moreover spectral analysis is made on a generalized time operator.
This work is supported by the Grant-in-Aid No.17340032 for Scientific Research from the JSPS. 相似文献
13.
We prove bounds on moments of the Smoluchowski coagulation equations with diffusion, in any dimension d ≥ 1. If the collision propensities α(n, m) of mass n and mass m particles grow more slowly than , and the diffusion rate is non-increasing and satisfies for some b
1 and b
2 satisfying 0 ≤ b
2 < b
1 < ∞, then any weak solution satisfies for every and T ∈(0, ∞), (provided that certain moments of the initial data are finite). As a consequence, we infer that these conditions
are sufficient to ensure uniqueness of a weak solution and its conservation of mass.
This work was performed while A.H. held a postdoctoral fellowship in the Department of Mathematics at U.B.C.
This work is supported in part by NSF grant DMS0307021. 相似文献
14.
H. -J. Grabosch H. H. Kaufmann U. Krecker R. Nahnhauer S. Nowak S. Schlenstedt H. Vogt E. P. Kuznetsov V. V. Ammosov D. S. Baranov V. I. Ermolaev A. A. Ivanilov P. V. Ivanov V. I. Konyushko V. M. Korablev V. A. Korotkov V. A. Krupnov V. V. Makeev A. G. Myagkov A. Yu. Polyarush A. A. Sokolov SKAT-Collaboration 《Zeitschrift fur Physik C Particles and Fields》1986,31(2):203-211
Studying the coherent diffractive production of pions in neutrino and antineutrino scattering off the nuclei of freon molecules we have observed for the first time in one experiment all three states of the isospin triplet of the axial part of the weak charged and neutral currents. For the corresponding cross sections we derive $$\begin{array}{*{20}c} {\sigma _{coh}^v (\pi ^ + ) = (106 \pm 16) \cdot 10^{ - 40} {{cm^2 } \mathord{\left/ {\vphantom {{cm^2 } {\left\langle {nucl.} \right\rangle }}} \right. \kern-\nulldelimiterspace} {\left\langle {nucl.} \right\rangle }}} \\ {\sigma _{coh}^{\bar v} (\pi ^ - ) = (113 \pm 35) \cdot 10^{ - 40} {{cm^2 } \mathord{\left/ {\vphantom {{cm^2 } {\left\langle {nucl.} \right\rangle }}} \right. \kern-\nulldelimiterspace} {\left\langle {nucl.} \right\rangle }}and} \\ {\sigma _{coh}^v (\pi ^0 ) = (52 \pm 19) \cdot 10^{ - 40} {{cm^2 } \mathord{\left/ {\vphantom {{cm^2 } {\left\langle {nucl.} \right\rangle }}} \right. \kern-\nulldelimiterspace} {\left\langle {nucl.} \right\rangle }}} \\ \end{array} $$ . Comparing our data with theoretical predictions based on the standard model of weak interactions we find reasonable agreement. Independently from any model of coherent pion production we determine the isovector axial vector coupling constant to be |β|=0.99±0.20. 相似文献
15.
Let denote the class of all orthomodular lattices and denote the class of those that are commutator-finite. Also, let denote the class of orthomodular lattices that satisfy the block extension property, those that satisfy the weak block extension property, and those that are locally finite. We show that the following strict containments hold:
Dedicated to the memory of Günter Bruns. 相似文献
16.
A Strong Szegő Theorem for Jacobi Matrices 总被引:1,自引:1,他引:0
E. Ryckman 《Communications in Mathematical Physics》2007,271(3):791-820
We use a classical result of Golinskii and Ibragimov to prove an analog of the strong Szegő theorem for Jacobi matrices on
. In particular, we consider the class of Jacobi matrices with conditionally summable parameter sequences and find necessary
and sufficient conditions on the spectral measure such that and lie in , the linearly-weighted l
2 space.
An erratum to this article can be found at 相似文献
17.
Luc Haine 《Letters in Mathematical Physics》2006,76(2-3):269-282
We give a new proof of a classical result of Lagnese and Stellmacher, characterizing all Huygens’ operators of the form
, where q(x) depends on only one variable. The proof amounts to characterize the Schrödinger operators
with a finite heat kernel expansion. 相似文献
18.
We prove that the spectrum of the discrete Schrödinger operator on ?2(?2) is absolutely continuous.
相似文献
$$\begin{array}{@{}rcl@{}} (\psi _{n,m})\mapsto -(\psi _{n + 1,m} +\psi _{n-1,m} + \psi _{n,m + 1} +\psi _{n,m-1})+V_{n}\psi _{n,m} \ , \\ \quad (n, m) \in \mathbb {Z}^{2},\ \left \{ V_{n}\right \}\in \ell ^{\infty }(\mathbb {Z}) \end{array} $$
(1)
19.
A. H. Khater M. S. Saif K. El. Rashidy 《International Journal of Theoretical Physics》2007,46(5):1124-1136
The aim of the present paper is to study the existence and the completeness of the wave operators for elliptic operators of higher order (Schr?dinger operator) with short-range potential of the form:
and other related results by using the trace class method.
MSC: 2000 46N50, 47Dxx, 47F05. 相似文献
20.
We present the main ingredients of twistor theory leading up to and including the Penrose-Ward transform in a coordinate algebra
form which we can then ‘quantise’ by means of a functorial cocycle twist. The quantum algebras for the conformal group, twistor
space , compactified Minkowski space and the twistor correspondence space are obtained along with their canonical quantum differential calculi, both in a local
form and in a global *-algebra formulation which even in the classical commutative case provides a useful alternative to the
formulation in terms of projective varieties. We outline how the Penrose-Ward transform then quantises. As an example, we
show that the pull-back of the tautological bundle on pulls back to the basic instanton on and that this observation quantises to obtain the Connes-Landi instanton on θ-deformed S
4 as the pull-back of the tautological bundle on our θ-deformed . We likewise quantise the fibration and use it to construct the bundle on θ-deformed that maps over under the transform to the θ-deformed instanton.
The work was mainly completed while S.M. was visiting July-December 2006 at the Isaac Newton Institute, Cambridge, which both
authors thank for support. 相似文献