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1.
We study the limit of quasilocal energy defined in Wang and Yau (Phys Rev Lett 102(2):021101, 2009; Commun Math Phys 288(3):919–942, 2009) for a family of spacelike 2-surfaces approaching null infinity of an asymptotically flat spacetime. It is shown that Lorentzian
symmetry is recovered and an energy-momentum 4-vector is obtained. In particular, the result is consistent with the Bondi–Sachs
energy-momentum at a retarded time. The quasilocal mass in Wang and Yau (Phys Rev Lett 102(2):021101, 2009; Commun Math Phys 288(3):919–942, 2009) is defined by minimizing quasilocal energy among admissible isometric embeddings and observers. The solvability of the Euler-Lagrange
equation for this variational problem is also discussed in both the asymptotically flat and asymptotically null cases. Assuming
analyticity, the equation can be solved and the solution is locally minimizing in all orders. In particular, this produces
an optimal reference hypersurface in the Minkowski space for the spatial or null exterior region of an asymptotically flat
spacetime. 相似文献
2.
The work by Ott et al. (Math. Res. Lett. 16:463–475, 2009) established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find
conditions under which we have convergence to the normal distribution of the appropriately scaled Birkhoff-like partial sums
of appropriate test functions. A substantial part of the problem is to ensure that the variances of the partial sums tend
to infinity (cf. the zero-cohomology condition in the autonomous case). In fact, the present paper is the first one where
non-random examples are also found, which are not small perturbations of a given map. Our approach uses martingale approximation
technique in the form of Sethuraman and Varadhan (Electron. J. Probab. 10:121–1235, 2005). 相似文献
3.
András Sütő 《Communications in Mathematical Physics》2011,305(3):657-710
Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize
the mean-field energy functional. By studying the latter we derive global properties of high-density ground state configurations
in bounded domains and in infinite space. Our main result is a theorem stating that for interactions having a strictly positive
Fourier transform the distribution of particles tends to be uniform as the density increases, while high-density ground states
show some pattern if the Fourier transform is partially negative. The latter confirms the conclusion of earlier studies by
Vlasov (in J. Phys. (USSR) IX:25–40, 1945), Kirzhnits and Nepomnyashchii (in Sov. Phys. JETP 32:1191–1197, 1971), and Likos et al. (in J. Chem. Phys. 126:224502, 2007). Other results include the proof that there is no Bravais lattice among high-density ground states of interactions whose
Fourier transform has a negative part and the potential diverges or has a cusp at zero. We also show that in the ground state
configurations of the penetrable sphere model particles are superimposed on the sites of a close-packed lattice. 相似文献
4.
The existence of a dynamo effect in a simplified magnetohydrodynamic model of turbulence is considered when the magnetic Prandtl
number approaches zero or infinity. The magnetic field is interacting with an incompressible Kraichnan-Kazantsev model velocity
field which incorporates also a viscous cutoff scale. An approximate system of equations in the different scaling ranges can
be formulated and solved, so that the solution tends to the exact one when the viscous and magnetic-diffusive cutoffs approach
zero. In this approximation we are able to determine analytically the conditions for the existence of a dynamo effect and
give an estimate of the dynamo growth rate. Among other things we show that in the large magnetic Prandtl number case the
dynamo effect is always present. Our analytical estimates are in good agreement with previous numerical studies of the Kraichnan-Kazantsev
dynamo by Vincenzi (J. Stat. Phys. 106:1073–1091, 2002). 相似文献
5.
6.
Subir Ghosh 《International Journal of Theoretical Physics》2011,50(11):3515-3520
In this note we have applied directly the Shannon formula for information theory entropy to derive the Black Hole (Bekenstein-Hawking)
entropy. Our analysis is semi-classical in nature since we use the (recently proposed Banerjee in Int. J. Mod. Phys. D 19:2365–2369,
2010 and Banerjee and Majhi in Phys. Rev. D 81:124006, 2010; Phys. Rev. D 79:064024, 2009; Phys. Lett. B 675:243, 2009) quantum mechanical near horizon mode functions to compute the tunneling probability that goes in to the Shannon formula,
following the general idea of Brillouin (Science and Information Theory, Dover, New York, 2004). Our framework conforms to the information theoretic origin of Black Hole entropy, as originally proposed by Bekenstein. 相似文献
7.
Roberto Beneduci 《International Journal of Theoretical Physics》2010,49(12):3030-3038
For each commutative POV measure F there exists (Beneduci, J. Math. Phys. 47:062104-1, 2006; Int. J. Geom. Methods Mod. Phys. 3:1559, 2006) a PV measure E such that F can be interpreted as a random diffusion of E. In its turn, the self-adjoint operator A=∫
λ
dE
λ
corresponding to E, can be interpreted (Beneduci, J. Math. Phys. 48:022102-1, 2007; Nuovo Cimento B 123:43–62, 2008) as the projection of a Naimark operator corresponding to the Naimark dilation E
+ of F. Moreover E can be algorithmically reconstructed by F. All that suggests that, in some sense, the observables represented by E and F should have the same informational content. We introduce an equivalence relation on the set of observables which we compare
with other well known equivalence relations and prove that it is the only one for which E is always equivalent to F. 相似文献
8.
9.
In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov
(Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic,
Norwell, 2004; Fuzzy Sets Syst. 155:4–17, 2005; Biosystems 84:225–241, 2006; Found. Phys. 35(10):1655–1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105–117, 2009), it was pointed out that statistics collected in such the experiments have “quantum-like” properties, which can not be explained
in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process
in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical
frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33–59, 1999). 相似文献
10.
Dong Wang 《International Journal of Theoretical Physics》2010,49(4):777-785
Based on Wu et al.’s original idea (Phys. Lett. A 372:2802, 2008), we propose a scheme to remotely implement multi-qubit quantum phase gates. With the assistance of entanglement swapping,
classical communication and quantum repeater, multi-qubit quantum phase gates can be realized perfectly nearly. It is emphasized
that our proposal can overcome the limitation that error probability scales exponentially with the length of the channel during
the realization of the gates. 相似文献
11.
We consider the KP-I and gKP-I equations in \mathbbR × (\mathbbR/2p\mathbbZ){{\mathbb{R}}\,\times\,({\mathbb{R}}/2\pi{\mathbb{Z}})}. We prove that the KdV soliton with subcritical speed 0 < c < c* is orbitally stable under the global KP-I flow constructed by Ionescu and Kenig (Ann Math Stud 163:181–211, 2007). For supercritical speeds c > c*, in the spirit of the work by Duyckaerts and Merle (GAFA 18:1787–1840, 2009), we sharpen our previous instability result and construct a global solution which is different from the solitary wave and its translates and which converges to the solitary wave as time goes to infinity. This last result also holds for the gKP-I equation. 相似文献
12.
Alessandro Pizzo David Renfrew Alexander Soshnikov 《Journal of statistical physics》2012,146(3):550-591
We study the fluctuations of the matrix entries of regular functions of Wigner random matrices in the limit when the matrix
size goes to infinity. In the case of the Gaussian ensembles (GOE and GUE) this problem was considered by A. Lytova and L.
Pastur (J. Stat. Phys. 134:147–159, 2009). Our results are valid provided the off-diagonal matrix entries have finite fourth moment, the diagonal matrix entries have
finite second moment, and the test functions have four continuous derivatives in a neighborhood of the support of the Wigner
semicircle law. Moreover, if the marginal distributions satisfy the Poincaré inequality our results are valid for Lipschitz
continuous test functions. 相似文献
13.
Mark J. Everitt 《Journal of Russian Laser Research》2009,30(5):412-417
We explore the quantum–classical crossover of two coupled, identical, superconducting quantum interference device (SQUID)
rings. The motivation for this work is based on a series of recent papers. In [1] we showed that the entanglement characteristics of chaotic and periodic (entrained) solutions of the Duffing oscillator
differed significantly and that in the classical limit entanglement was preserved only in the chaotic-like solutions. However,
Duffing oscillators are a highly idealized toy system. Motivated by a wish to explore more experimentally realizable systems,
we extended our work in [2, 3] to an analysis of SQUID rings. In [3] we showed that the two systems share a common feature. That is, when the SQUID ring’s trajectories appear to follow (semi)classical
orbits, entanglement persists. Our analysis in [3] was restricted to the quantum-state diffusion unraveling of the master equation – representing unit efficiency heterodyne
detection (or ambi-quadrature homodyne detection). Here we show that very similar behavior occurs using the quantum jumps
unraveling of the master equation. Quantum jumps represents a discontinuous photon counting measurement process. Hence, the
results presented here imply that such persistent entanglement is independent of measurement process and that our results
may well be quite general in nature. 相似文献
14.
A Fredholm Determinant Representation in ASEP 总被引:3,自引:2,他引:1
In previous work (Tracy and Widom in Commun. Math. Phys. 279:815–844, 2008) the authors found integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice
ℤ. The dynamics are uniquely determined once the initial state is specified. In this note we restrict our attention to the
case of step initial condition with particles at the positive integers ℤ+ and consider the distribution function for the mth particle from the left. In Tracy and Widom (Commun. Math. Phys. 279:815–844, 2008) an infinite series of multiple integrals was derived for the distribution. In this note we show that the series can be summed
to give a single integral whose integrand involves a Fredholm determinant. We use this determinant representation to derive
(non-rigorously, at this writing) a scaling limit. 相似文献
15.
Su-Juan Qin 《International Journal of Theoretical Physics》2012,51(9):2714-2718
A controlled quantum secure direct communication protocol (Zhang et al. in Int. J. Theor. Phys. 48:2971–2976, 2009) by using four particle cluster states was proposed recently. Yang et al. presented an attack with fake entangled particles (FEP attack) and gave an improvement (Yang et al. in Int. J. Theor. Phys. 50:395–400, 2010). In this paper, we reexamine the protocol’s security and discover that, Bob can also take a different attack, disentanglement attack, to obtain Alice’s secret message without controller’s permission. Moreover, our attack strategy also works for Yang’s improvement. 相似文献
16.
17.
The regularized determinant of the Paneitz operator arises in quantum gravity [see Connes in (Noncommutative geometry, 1994), IV.4.γ]. An explicit formula for the relative determinant of two conformally related metrics was computed by Branson in (Commun Math Phys 178:301–309, 1996). A similar formula holds for Cheeger’s half-torsion, which plays a role in self-dual field theory [see Juhl in (Families of conformally covariant differential operators, q-curvature and holography. Progress in Mathematics, vol 275, 2009)], and is defined in terms of regularized determinants of the Hodge laplacian on p-forms (p < n/2). In this article we show that the corresponding actions are unbounded (above and below) on any conformal four-manifold. We also show that the conformal class of the round sphere admits a second solution which is not given by the pull-back of the round metric by a conformal map, thus violating uniqueness up to gauge equivalence. These results differ from the properties of the determinant of the conformal Laplacian established in (Commun Math Phys 149:241–262, 1992), (Ann Math 142:171–212, 1995), (Commun Math Phys 189:655–665, 1997). 相似文献
18.
19.
In this paper, we generalize the Kirchhoff-Sobolev parametrix of Klainerman and Rodnianski (Hyperbolic Equ. 4(3):401–433,
2007) to systems of tensor wave equations with additional first-order terms. We also present a different derivation, which better
highlights that such representation formulas are supported entirely on past null cones. This generalization of (Hyperbolic
Equ. 4(3):401–433, 2007) is a key component for extending Klainerman and Rodnianski’s breakdown criterion result for Einstein-vacuum spacetimes in
(J. Amer. Math. Soc. 23(2):345–382, 2009) to Einstein-Maxwell and Einstein-Yang-Mills spacetimes. 相似文献