@article{9973,
abstract = {In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors.},
author = {Wirth, Melchior and Zhang, Haonan},
issn = {1432-0916},
journal = {Communications in Mathematical Physics},
keywords = {Mathematical Physics, Statistical and Nonlinear Physics},
publisher = {Springer Nature},
title = {{Complete gradient estimates of quantum Markov semigroups}},
doi = {10.1007/s00220-021-04199-4},
year = {2021},
}
@article{6185,
abstract = {For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969).},
author = {Erdös, László and Krüger, Torben H and Schröder, Dominik J},
issn = {1432-0916},
journal = {Communications in Mathematical Physics},
pages = {1203--1278},
publisher = {Springer Nature},
title = {{Cusp universality for random matrices I: Local law and the complex Hermitian case}},
doi = {10.1007/s00220-019-03657-4},
volume = {378},
year = {2020},
}
@article{6649,
abstract = {While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.
},
author = {Benedikter, Niels P and Nam, Phan Thành and Porta, Marcello and Schlein, Benjamin and Seiringer, Robert},
issn = {1432-0916},
journal = {Communications in Mathematical Physics},
pages = {2097–2150},
publisher = {Springer Nature},
title = {{Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime}},
doi = {10.1007/s00220-019-03505-5},
volume = {374},
year = {2020},
}
@article{7004,
abstract = {We define an action of the (double of) Cohomological Hall algebra of Kontsevich and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov. We identify this action with the one of the affine Yangian of gl(1). Based on that we derive the vertex algebra at the corner Wr1,r2,r3 of Gaiotto and Rapčák. We conjecture that our approach works for a big class of Calabi–Yau categories, including those associated with toric Calabi–Yau 3-folds.},
author = {Rapcak, Miroslav and Soibelman, Yan and Yang, Yaping and Zhao, Gufang},
issn = {1432-0916},
journal = {Communications in Mathematical Physics},
pages = {1803--1873},
publisher = {Springer Nature},
title = {{Cohomological Hall algebras, vertex algebras and instantons}},
doi = {10.1007/s00220-019-03575-5},
volume = {376},
year = {2020},
}
@article{8415,
abstract = {We consider billiards obtained by removing three strictly convex obstacles satisfying the non-eclipse condition on the plane. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift on three symbols that provides a natural labeling of all periodic orbits. We study the following inverse problem: does the Marked Length Spectrum (i.e., the set of lengths of periodic orbits together with their labeling), determine the geometry of the billiard table? We show that from the Marked Length Spectrum it is possible to recover the curvature at periodic points of period two, as well as the Lyapunov exponent of each periodic orbit.},
author = {Bálint, Péter and De Simoi, Jacopo and Kaloshin, Vadim and Leguil, Martin},
issn = {0010-3616},
journal = {Communications in Mathematical Physics},
keywords = {Mathematical Physics, Statistical and Nonlinear Physics},
number = {3},
pages = {1531--1575},
publisher = {Springer Nature},
title = {{Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards}},
doi = {10.1007/s00220-019-03448-x},
volume = {374},
year = {2019},
}
@article{6906,
abstract = {We consider systems of bosons trapped in a box, in the Gross–Pitaevskii regime. We show that low-energy states exhibit complete Bose–Einstein condensation with an optimal bound on the number of orthogonal excitations. This extends recent results obtained in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018), removing the assumption of small interaction potential.},
author = {Boccato, Chiara and Brennecke, Christian and Cenatiempo, Serena and Schlein, Benjamin},
issn = {0010-3616},
journal = {Communications in Mathematical Physics},
pages = {1311--1395},
publisher = {Springer},
title = {{Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime}},
doi = {10.1007/s00220-019-03555-9},
volume = {376},
year = {2019},
}
@article{7100,
abstract = {We present microscopic derivations of the defocusing two-dimensional cubic nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting froman interacting N-particle system of bosons. We consider the interaction potential to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx), for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R). In both cases we prove the convergence of the reduced density corresponding to the exact time evolution to the projector onto the solution of the corresponding nonlinear Schrödinger equation in trace norm. For the latter potential VN we show that it is crucial to take the microscopic structure of the condensate into account in order to obtain the correct dynamics.},
author = {Jeblick, Maximilian and Leopold, Nikolai K and Pickl, Peter},
issn = {1432-0916},
journal = {Communications in Mathematical Physics},
number = {1},
pages = {1--69},
publisher = {Springer Nature},
title = {{Derivation of the time dependent Gross–Pitaevskii equation in two dimensions}},
doi = {10.1007/s00220-019-03599-x},
volume = {372},
year = {2019},
}
@article{8417,
abstract = {The restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet or an asteroid) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of mass on elliptic orbits with some positive eccentricity. The aim of this paper is to show the existence of orbits whose angular momentum performs arbitrary excursions in a large region. In particular, there exist diffusive orbits, that is, with a large variation of angular momentum. The leading idea of the proof consists in analyzing parabolic motions of the comet. By a well-known result of McGehee, the union of future (resp. past) parabolic orbits is an analytic manifold P+ (resp. P−). In a properly chosen coordinate system these manifolds are stable (resp. unstable) manifolds of a manifold at infinity P∞, which we call the manifold at parabolic infinity. On P∞ it is possible to define two scattering maps, which contain the map structure of the homoclinic trajectories to it, i.e. orbits parabolic both in the future and the past. Since the inner dynamics inside P∞ is trivial, two different scattering maps are used. The combination of these two scattering maps permits the design of the desired diffusive pseudo-orbits. Using shadowing techniques and these pseudo orbits we show the existence of true trajectories of the RPETBP whose angular momentum varies in any predetermined fashion.},
author = {Delshams, Amadeu and Kaloshin, Vadim and de la Rosa, Abraham and Seara, Tere M.},
issn = {0010-3616},
journal = {Communications in Mathematical Physics},
keywords = {Mathematical Physics, Statistical and Nonlinear Physics},
number = {3},
pages = {1173--1228},
publisher = {Springer Nature},
title = {{Global instability in the restricted planar elliptic three body problem}},
doi = {10.1007/s00220-018-3248-z},
volume = {366},
year = {2018},
}
@article{8493,
abstract = {In this paper we study a so-called separatrix map introduced by Zaslavskii–Filonenko (Sov Phys JETP 27:851–857, 1968) and studied by Treschev (Physica D 116(1–2):21–43, 1998; J Nonlinear Sci 12(1):27–58, 2002), Piftankin (Nonlinearity (19):2617–2644, 2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3–108, 2007). We derive a second order expansion of this map for trigonometric perturbations. In Castejon et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint available at arXiv:1501.03319, 2015), Guardia and Kaloshin (Stochastic diffusive behavior through big gaps in a priori unstable systems (in preparation), 2015), and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior for the generalized Arnold example away from resonances. Preprint available at http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present paper, we describe a class of nearly integrable deterministic systems with stochastic diffusive behavior.},
author = {Guardia, M. and Kaloshin, Vadim and Zhang, J.},
issn = {0010-3616},
journal = {Communications in Mathematical Physics},
pages = {321--361},
publisher = {Springer Nature},
title = {{A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems}},
doi = {10.1007/s00220-016-2705-9},
volume = {348},
year = {2016},
}
@article{8502,
abstract = {The famous ergodic hypothesis suggests that for a typical Hamiltonian on a typical energy surface nearly all trajectories are dense. KAM theory disproves it. Ehrenfest (The Conceptual Foundations of the Statistical Approach in Mechanics. Ithaca, NY: Cornell University Press, 1959) and Birkhoff (Collected Math Papers. Vol 2, New York: Dover, pp 462–465, 1968) stated the quasi-ergodic hypothesis claiming that a typical Hamiltonian on a typical energy surface has a dense orbit. This question is wide open. Herman (Proceedings of the International Congress of Mathematicians, Vol II (Berlin, 1998). Doc Math 1998, Extra Vol II, Berlin: Int Math Union, pp 797–808, 1998) proposed to look for an example of a Hamiltonian near H0(I)=⟨I,I⟩2 with a dense orbit on the unit energy surface. In this paper we construct a Hamiltonian H0(I)+εH1(θ,I,ε) which has an orbit dense in a set of maximal Hausdorff dimension equal to 5 on the unit energy surface.},
author = {Kaloshin, Vadim and Saprykina, Maria},
issn = {0010-3616},
journal = {Communications in Mathematical Physics},
keywords = {Mathematical Physics, Statistical and Nonlinear Physics},
number = {3},
pages = {643--697},
publisher = {Springer Nature},
title = {{An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension}},
doi = {10.1007/s00220-012-1532-x},
volume = {315},
year = {2012},
}
@article{8525,
abstract = {Let M be a smooth compact manifold of dimension at least 2 and Diffr(M) be the space of C r smooth diffeomorphisms of M. Associate to each diffeomorphism f;isin; Diffr(M) the sequence P n (f) of the number of isolated periodic points for f of period n. In this paper we exhibit an open set N in the space of diffeomorphisms Diffr(M) such for a Baire generic diffeomorphism f∈N the number of periodic points P n f grows with a period n faster than any following sequence of numbers {a n } n ∈ Z + along a subsequence, i.e. P n (f)>a ni for some n i →∞ with i→∞. In the cases of surface diffeomorphisms, i.e. dim M≡2, an open set N with a supergrowth of the number of periodic points is a Newhouse domain. A proof of the man result is based on the Gontchenko–Shilnikov–Turaev Theorem [GST]. A complete proof of that theorem is also presented.},
author = {Kaloshin, Vadim},
issn = {0010-3616},
journal = {Communications in Mathematical Physics},
keywords = {Mathematical Physics, Statistical and Nonlinear Physics},
pages = {253--271},
publisher = {Springer Nature},
title = {{Generic diffeomorphisms with superexponential growth of number of periodic orbits}},
doi = {10.1007/s002200050811},
volume = {211},
year = {2000},
}