共查询到20条相似文献,搜索用时 15 毫秒
1.
We study the existence and uniqueness of the time evolution via the Newton law of a two dimensional system of infinitely many
particles with very singular mutual interactions. It is an improvement of the result by Fritz and Dobrushin given in (Comm.
Math. Phys. 57:67–81, 1977) for inverse power-like singular interactions. 相似文献
2.
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
3.
In this paper we study the asymptotic behavior (in the sense of meromorphic functions) of the zeta function of a Laplace-type
operator on a closed manifold when the underlying manifold is stretched in the direction normal to a dividing hypersurface,
separating the manifold into two manifolds with infinite cylindrical ends. We also study the related problem on a manifold
with boundary as the manifold is stretched in the direction normal to its boundary, forming a manifold with an infinite cylindrical
end. Such singular deformations fall under the category of “analytic surgery”, developed originally by Hassell (Comm Anal
Geom 6:255–289, 1998), Hassell et al. (Comm Anal Geom 3:115–222, 1995) and Mazzeo and Melrose (Geom Funct Anal 5:14–75, 1995) in the context of eta invariants and determinants. 相似文献
4.
In this paper, we study the macroscopic limit of a new model of collective displacement. The model, called PTWA, is a combination
of the Vicsek alignment model (Vicsek et al. in Phys. Rev. Lett. 75(6):1226–1229, 1995) and the Persistent Turning Walker (PTW) model of motion by curvature control (Degond and Motsch in J. Stat. Phys. 131(6):989–1021,
2008; Gautrais et al. in J. Math. Biol. 58(3):429–445, 2009). The PTW model was designed to fit measured trajectories of individual fish (Gautrais et al. in J. Math. Biol. 58(3):429–445,
2009). The PTWA model (Persistent Turning Walker with Alignment) describes the displacements of agents which modify their curvature
in order to align with their neighbors. The derivation of its macroscopic limit uses the non-classical notion of generalized
collisional invariant introduced in (Degond and Motsch in Math. Models Methods Appl. Sci. 18(1):1193–1215, 2008). The macroscopic limit of the PTWA model involves two physical quantities, the density and the mean velocity of individuals.
It is a system of hyperbolic type but is non-conservative due to a geometric constraint on the velocity. This system has the
same form as the macroscopic limit of the Vicsek model (Degond and Motsch in Math. Models Methods Appl. Sci. 18(1):1193–1215,
2008) (the ‘Vicsek hydrodynamics’) but for the expression of the model coefficients. The numerical computations show that the
numerical values of the coefficients are very close. The ‘Vicsek Hydrodynamic model’ appears in this way as a more generic
macroscopic model of swarming behavior as originally anticipated. 相似文献
5.
Xicheng Zhang 《Communications in Mathematical Physics》2012,311(1):133-155
In this article we study the fractal Navier-Stokes equations by using the stochastic Lagrangian particle path approach in
Constantin and Iyer (Comm Pure Appl Math LXI:330–345, 2008). More precisely, a stochastic representation for the fractal Navier-Stokes equations is given in terms of stochastic differential
equations driven by Lévy processes. Based on this representation, a self-contained proof for the existence of a local unique
solution for the fractal Navier-Stokes equation with initial data in
\mathbb W1,p{{\mathbb W}^{1,p}} is provided, and in the case of two dimensions or large viscosity, the existence of global solutions is also obtained. In
order to obtain the global existence in any dimensions for large viscosity, the gradient estimates for Lévy processes with
time dependent and discontinuous drifts are proved. 相似文献
6.
Quantum computational logics have recently stirred increasing attention (Cattaneo et al. in Math. Slovaca 54:87–108, 2004; Ledda et al. in Stud. Log. 82(2):245–270, 2006; Giuntini et al. in Stud. Log. 87(1):99–128, 2007). In this paper we outline their motivations and report on the state of the art of the approach to the logic of quantum computation
that has been recently taken up and developed by our research group. 相似文献
7.
8.
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
9.
Federico Bassetti Lucia Ladelli Giuseppe Toscani 《Journal of statistical physics》2011,142(4):686-709
We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules which, in some
special cases, identify models for granular gases with a background heat bath (Carrillo et al. in Discrete Contin. Dyn. Syst.
24(1):59–81, 2009), and models for wealth redistribution in an agent-based market (Bisi et al. in Commun. Math. Sci. 7:901–916, 2009). Conditions on these collisional rules which guarantee both the existence and uniqueness of equilibrium profiles and their
main properties are found. The characterization of these stationary states is of independent interest, since we show that
they are stationary solutions of different evolution problems, both in the kinetic theory of rarefied gases (Cercignani et al.
in J. Stat. Phys. 105:337–352, 2001; Villani in J. Stat. Phys. 124:781–822, 2006) and in the econophysical context (Bisi et al. in Commun. Math. Sci. 7:901–916, 2009). 相似文献
10.
Paweł Góra Zhenyang Li Abraham Boyarsky Harald Proppe 《Journal of statistical physics》2012,146(4):850-863
The statistical behavior of families of maps is important in studying the stability properties of chaotic maps. For a piecewise
expanding map τ whose slope >2 in magnitude, much is known about the stability of the associated invariant density. However, when the map
has slope magnitude ≤2 many different behaviors can occur as shown in (Keller in Monatsh. Math. 94(4): 313–333, 1982) for W maps. The main results of this note use a harmonic average of slopes condition to obtain new explicit constants for
the upper and lower bounds of the invariant probability density function associated with the map, as well as a bound for the
speed of convergence to the density. Since these constants are determined explicitly the results can be extended to families
of approximating maps. 相似文献
11.
Peter Nyman 《International Journal of Theoretical Physics》2010,49(1):1-9
In this paper we continue to study so-called “inverse Born’s rule problem”: to construct a representation of probabilistic
data of any origin by a complex probability amplitude which matches Born’s rule. The corresponding algorithm—quantum-like
representation algorithm (QLRA)—was recently proposed by A. Khrennikov (Found. Phys. 35(10):1655–1693, 2005; Physica E 29:226–236, 2005; Dokl. Akad. Nauk 404(1):33–36, 2005; J. Math. Phys. 46(6):062111–062124, 2005; Europhys. Lett. 69(5):678–684, 2005). Formally QLRA depends on the order of conditioning. For two observables (of any origin, e.g., physical or biological) a and b, b|a- and a|b conditional probabilities produce two representations, say in Hilbert spaces H
b|a
and H
a|b
. In this paper we prove that under “natural assumptions” (which hold, e.g., for quantum observables represented by operators
with nondegenerate spectra) these two representations are unitary equivalent. This result proves the consistency of QLRA. 相似文献
12.
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
13.
A lifting is a map from the state of a system to that of a compound system, which was introduced in Accardi and Ohya (Appl.
Math. Optim. 39:33–59, 1999). The lifting can be applied to various physical processes. 相似文献
14.
15.
Yaacov Kopeliovich 《Letters in Mathematical Physics》2010,94(3):313-333
Let X be a general cyclic cover of
\mathbbCP1{\mathbb{CP}^{1}} ramified at m points, λ1... λ
m
. we define a class of non-positive divisors on X of degree g −1 supported in the pre images of the branch points on X, such that the Riemann theta function does not vanish on their image in J(X). We generalize the results of Bershadsky and Radul (Commun Math Phys 116:689–700, 1988), Nakayashiki (Publ Res Inst Math Sci 33(6):987–1015, 1997) and Enolskii and Grava (Lett Math Phys 76(2–3):187–214, 2006) and prove that up to a certain determinant of the non-standard periods of X, the value of the Riemann theta function at these divisors raised to a high enough power is a polynomial in the branch point
of the curve X. Our approach is based on a refinement of Accola’s results for 3 cyclic sheeted cover (Accola, in Trans Am Math Soc 283:423–449,
1984) and a generalization of Nakayashiki’s approach explained in Nakayashiki (Publ Res Inst Math Sci 33(6):987–1015, 1997) for general cyclic covers. 相似文献
16.
Tuyen Trung Truong 《Mathematical Physics, Analysis and Geometry》2009,12(2):157-180
We determine the degree complexity for all elements of a family k
F
of birational maps which was introduced and studied in Bedford et al. (Math Phys Anal Geom 11:53–71, 2008).
相似文献
17.
E. Ryckman 《Journal of statistical physics》2008,132(3):473-486
For arbitrary β>0, we use the orthogonal polynomials techniques developed in (Killip and Nenciu in , 2005; Killip and Nenciu in Int. Math. Res. Not. 50: 2665–2701, 2004) to study certain linear statistics associated with the circular and Jacobi β ensembles. We identify the distribution of these statistics then prove a joint central limit theorem. In the circular case,
similar statements have been proved using different methods by a number of authors. In the Jacobi case these results are new. 相似文献
18.
Anatoliy K. Prykarpatsky Nikolai N. Bogolubov 《International Journal of Theoretical Physics》2012,51(1):237-245
R. Feynman’s “heretical” approach (Dyson in Am. J. Phys. 58:209–211, 1990; Dyson in Phys. Today 42(2):32–38, 1989) to deriving the Lorentz force based Maxwell electromagnetic equations is revisited, the its complete legacy is argued both
by means of the geometric considerations and its deep relation with the vacuum field theory approach devised (Prykarpatsky
et al. in Int. J. Theor. Phys. 49:798–820, 2010; Prykarpatsky et al. in Preprint ICTP, 2008, ). Being completely classical, we reanalyze the Feynman’s derivation from the classical Lagrangian and Hamiltonian points
of view and construct its nontrivial relativistic generalization compatible with the vacuum field theory approach. 相似文献
19.
The present work establishes the mean-field limit of a N-particle system towards a regularized variant of the relativistic Vlasov-Maxwell system, following the work of Braun-Hepp
[Commun Math Phys 56:101–113, 1977] and Dobrushin [Func Anal Appl 13:115–123, 1979] for the Vlasov-Poisson system. The main ingredients in the analysis of this system are (a) a kinetic formulation of the
Maxwell equations in terms of a distribution of electromagnetic potential in the momentum variable, (b) a regularization procedure
for which an analogue of the total energy—i.e. the kinetic energy of the particles plus the energy of the electromagnetic
field—is conserved and (c) an analogue of Dobrushin’s stability estimate for the Monge-Kantorovich-Rubinstein distance between
two solutions of the regularized Vlasov-Poisson dynamics adapted to retarded potentials. 相似文献
20.
We analyze the large-time behavior of various kinetic models for the redistribution of wealth in simple market economies introduced
in the pertinent literature in recent years. As specific examples, we study models with fixed saving propensity introduced
by Chakraborti and Chakrabarti (Eur. Phys. J. B 17:167–170, 2000), as well as models involving both exchange between agents and speculative trading as considered by Cordier et al. (J. Stat.
Phys. 120:253–277, 2005) We derive a sufficient criterion under which a unique non-trivial stationary state exists, and provide criteria under which
these steady states do or do not possess a Pareto tail. In particular, we prove the absence of Pareto tails in pointwise conservative
models, like the one in (Eur. Phys. J. B 17:167–170, 2000), while models with speculative trades introduced in (J. Stat. Phys. 120:253–277, 2005) develop fat tails if the market is “risky enough”. The results are derived by a Fourier-based technique first developed
for the Maxwell-Boltzmann equation (Gabetta et al. in J. Stat. Phys. 81:901–934, 1995; Bisi et al. in J. Stat. Phys. 118(1–2):301–331, 2005; Pareschi and Toscani in J. Stat. Phys. 124(2–4):747–779, 2006) and from a recursive relation which allows to calculate arbitrary moments of the stationary state. 相似文献