@article{22813,
  abstract     = {Consider a bipartite quantum system, where Alice and Bob jointly possess
a pure state |ψ. Using local quantum operations on their respective subsystems, and
unlimited classical communication, Alice and Bob may be able to transform |ψ into
another state |φ. Famously, Nielsen’s theorem [28] provides a necessary and sufficient
algebraic criterion for such a transformation to be possible (namely, the entanglement
spectrum of |φ should majorise the entanglement spectrum of |ψ). In the paper where
Nielsen proved this theorem, he conjectured that in the limit of large dimensionality, for
almost all pairs of states |ψ, |φ (according to the natural unitary invariant measure) such
a transformation is not possible. That is to say, typical pairs of quantum states |ψ, |φ
are entangled in fundamentally different ways, that cannot be converted to each other via
local operations and classical communication.ViaNielsen’s theorem, this conjecture can
be equivalently stated as a conjecture about majorisation of spectra of random matrices
from the so-called trace-normalised complex Wishart–Laguerre ensemble. Concretely,
let X and Y be independent n × m random matrices whose entries are i.i.d. standard
complex Gaussians; then Nielsen’s conjecture says that the probability that the spectrum
of XX†/ tr(XX†) majorises the spectrum of YY†/ tr(YY†) tends to zero as both n and
m grow large. We prove this conjecture, and we also confirm some related predictions
of Cunden et al. [12].},
  author       = {Jain, Vishesh and Kwan, Matthew Alan and Michelen, Marcus},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  number       = {10},
  publisher    = {Springer},
  title        = {{Entangled states are typically incomparable}},
  doi          = {10.1007/s00220-026-05711-4},
  volume       = {407},
  year         = {2026},
}

@article{19625,
  abstract     = {We introduce operator-valued twisted Araki–Woods algebras. These are operator-valued versions of a class of second quantization algebras that includes q-Gaussian and q-Araki–Woods algebras and also generalize Shlyakhtenko’s von Neumann algebras generated by operator-valued semicircular variables. We develop a disintegration theory that reduces the isomorphism type of operator-valued twisted Araki–Woods algebras over type I factors to the scalar-valued case. Moreover, these algebras come with a natural weight, and we characterize its modular theory. We also give sufficient criteria that guarantee the factoriality of these algebras.},
  author       = {Kumar, R. Rahul and Wirth, Melchior},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  number       = {5},
  publisher    = {Springer Nature},
  title        = {{Operator-valued twisted Araki–Woods algebras}},
  doi          = {10.1007/s00220-025-05285-7},
  volume       = {406},
  year         = {2025},
}

@article{20322,
  abstract     = {For correlated real symmetric or complex Hermitian random matrices, we prove that the local eigenvalue statistics at any cusp singularity are universal. Since the density of states typically exhibits only square root edge or cubic root cusp singularities, our result completes the proof of the Wigner–Dyson–Mehta universality conjecture in all spectral regimes for a very general class of random matrices. Previously only the bulk and the edge universality were established in this generality (Alt et al. in Ann Probab 48(2):963–1001, 2020), while cusp universality was proven only for Wigner-type matrices with independent entries (Cipolloni et al. in Pure Appl Anal 1:615–707, 2019; Erdős et al. in Commun. Math. Phys. 378:1203–1278, 2018). As our main technical input, we prove an optimal local law at the cusp using the <jats:italic>Zigzag strategy</jats:italic>, a recursive tandem of the characteristic flow method and a Green function comparison argument. Moreover, our proof of the optimal local law holds uniformly in the spectrum, thus we also provide a significantly simplified alternative proof of the local eigenvalue universality in the previously studied bulk (Erdős et al. in Forum Math. Sigma 7:E8, 2019) and edge (Alt et al. in Ann Probab 48(2):963–1001, 2020) regimes.},
  author       = {Erdös, László and Henheik, Sven Joscha and Riabov, Volodymyr},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  number       = {10},
  publisher    = {Springer Nature},
  title        = {{Cusp universality for correlated random matrices}},
  doi          = {10.1007/s00220-025-05417-z},
  volume       = {406},
  year         = {2025},
}

@article{15350,
  abstract     = {We extend three related results from the analysis of influences of Boolean functions to the quantum setting, namely the KKL theorem, Friedgut’s Junta theorem and Talagrand’s variance inequality for geometric influences. Our results are derived by a joint use of recently studied hypercontractivity and gradient estimates. These generic tools also allow us to derive generalizations of these results in a general von Neumann algebraic setting beyond the case of the quantum hypercube, including examples in infinite dimensions relevant to quantum information theory such as continuous variables quantum systems. Finally, we comment on the implications of our results as regards to noncommutative extensions of isoperimetric type inequalities, quantum circuit complexity lower bounds and the learnability of quantum observables.},
  author       = {Rouzé, Cambyse and Wirth, Melchior and Zhang, Haonan},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  number       = {4},
  publisher    = {Springer Nature},
  title        = {{Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum boolean functions}},
  doi          = {10.1007/s00220-024-04981-0},
  volume       = {405},
  year         = {2024},
}

@article{18554,
  abstract     = {We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for obs ervables of arbitrary rank. As the main technical ingredient, we prove rank-uniform optimal local laws for one and two resolvents of a Wigner-type matrix with regular observables. Our results hold under very general conditions on the variance profile, even allowing many vanishing entries, demonstrating that Eigenstate Thermalization occurs robustly across a diverse class of random matrix ensembles, for which the underlying quantum system has a non-trivial spatial structure.},
  author       = {Erdös, László and Riabov, Volodymyr},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  number       = {12},
  publisher    = {Springer Nature},
  title        = {{Eigenstate Thermalization Hypothesis for Wigner-type matrices}},
  doi          = {10.1007/s00220-024-05143-y},
  volume       = {405},
  year         = {2024},
}

@article{12792,
  abstract     = {In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disordered quantum systems, yet previous mathematical results have been restricted only to two exactly solvable models (Forrester in J Stat Phys 183:33, 2021. https://doi.org/10.1007/s10955-021-02767-5, Commun Math Phys 387:215–235, 2021. https://doi.org/10.1007/s00220-021-04193-w). We rigorously prove the physics prediction on SFF up to an intermediate time scale for a large class of random matrices using a robust method, the multi-resolvent local laws. Beyond Wigner matrices we also consider the monoparametric ensemble and prove that universality of SFF can already be triggered by a single random parameter, supplementing the recently proven Wigner–Dyson universality (Cipolloni et al. in Probab Theory Relat Fields, 2021. https://doi.org/10.1007/s00440-022-01156-7) to larger spectral scales. Remarkably, extensive numerics indicates that our formulas correctly predict the SFF in the entire slope-dip-ramp regime, as customarily called in physics.},
  author       = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  pages        = {1665--1700},
  publisher    = {Springer Nature},
  title        = {{On the spectral form factor for random matrices}},
  doi          = {10.1007/s00220-023-04692-y},
  volume       = {401},
  year         = {2023},
}

@article{13319,
  abstract     = {We prove that the generator of the L2 implementation of a KMS-symmetric quantum Markov semigroup can be expressed as the square of a derivation with values in a Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially symmetric semigroups and the second-named author for GNS-symmetric semigroups. This result hinges on the introduction of a new completely positive map on the algebra of bounded operators on the GNS Hilbert space. This transformation maps symmetric Markov operators to symmetric Markov operators and is essential to obtain the required inner product on the Hilbert bimodule.},
  author       = {Vernooij, Matthijs and Wirth, Melchior},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  pages        = {381--416},
  publisher    = {Springer Nature},
  title        = {{Derivations and KMS-symmetric quantum Markov semigroups}},
  doi          = {10.1007/s00220-023-04795-6},
  volume       = {403},
  year         = {2023},
}

@article{14427,
  abstract     = {In the paper, we establish Squash Rigidity Theorem—the dynamical spectral rigidity for piecewise analytic Bunimovich squash-type stadia whose convex arcs are homothetic. We also establish Stadium Rigidity Theorem—the dynamical spectral rigidity for piecewise analytic Bunimovich stadia whose flat boundaries are a priori fixed. In addition, for smooth Bunimovich squash-type stadia we compute the Lyapunov exponents along the maximal period two orbit, as well as the value of the Peierls’ Barrier function from the maximal marked length spectrum associated to the rotation number 2n/4n+1.},
  author       = {Chen, Jianyu and Kaloshin, Vadim and Zhang, Hong Kun},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  pages        = {1--50},
  publisher    = {Springer Nature},
  title        = {{Length spectrum rigidity for piecewise analytic Bunimovich billiards}},
  doi          = {10.1007/s00220-023-04837-z},
  volume       = {404},
  year         = {2023},
}

@article{14441,
  abstract     = {We study the Fröhlich polaron model in R3, and establish the subleading term in the strong coupling asymptotics of its ground state energy, corresponding to the quantum corrections to the classical energy determined by the Pekar approximation.},
  author       = {Brooks, Morris and Seiringer, Robert},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  pages        = {287--337},
  publisher    = {Springer Nature},
  title        = {{The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy}},
  doi          = {10.1007/s00220-023-04841-3},
  volume       = {404},
  year         = {2023},
}

@article{11332,
  abstract     = {We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size N converge to the Tracy–Widom laws at a rate O(N^{-1/3+\omega }), as N tends to infinity. For Wigner matrices this improves the previous rate O(N^{-2/9+\omega }) obtained by Bourgade (J Eur Math Soc, 2021) for generalized Wigner matrices. Our result follows from a Green function comparison theorem, originally introduced by Erdős et al. (Adv Math 229(3):1435–1515, 2012) to prove edge universality, on a finer spectral parameter scale with improved error estimates. The proof relies on the continuous Green function flow induced by a matrix-valued Ornstein–Uhlenbeck process. Precise estimates on leading contributions from the third and fourth order moments of the matrix entries are obtained using iterative cumulant expansions and recursive comparisons for correlation functions, along with uniform convergence estimates for correlation kernels of the Gaussian invariant ensembles.},
  author       = {Schnelli, Kevin and Xu, Yuanyuan},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  pages        = {839--907},
  publisher    = {Springer Nature},
  title        = {{Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices}},
  doi          = {10.1007/s00220-022-04377-y},
  volume       = {393},
  year         = {2022},
}

@article{22043,
  abstract     = {We prove that multisoliton solutions of the Korteweg–de Vries equation are orbitally stable in H^-1(R). We introduce a variational characterization of multisolitons that remains meaningful at such low regularity and show that all optimizing sequences converge to the manifold of multisolitons. The proximity required at the initial time is uniform across the entire manifold of multisolitons; this had not been demonstrated previously, even in H^-1.},
  author       = {Killip, Rowan and Visan, Monica},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  number       = {3},
  pages        = {1445--1473},
  publisher    = {Springer Nature},
  title        = {{Orbital stability of KdV multisolitons in H-1}},
  doi          = {10.1007/s00220-021-04280-y},
  volume       = {389},
  year         = {2022},
}

@article{10221,
  abstract     = {We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020).},
  author       = {Cipolloni, Giorgio and Erdös, László and Schröder, Dominik J},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  number       = {2},
  pages        = {1005–1048},
  publisher    = {Springer Nature},
  title        = {{Eigenstate thermalization hypothesis for Wigner matrices}},
  doi          = {10.1007/s00220-021-04239-z},
  volume       = {388},
  year         = {2021},
}

@article{8816,
  abstract     = {Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.},
  author       = {Runkel, Ingo and Szegedy, Lorant},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  number       = {1},
  pages        = {83–117},
  publisher    = {Springer Nature},
  title        = {{Area-dependent quantum field theory}},
  doi          = {10.1007/s00220-020-03902-1},
  volume       = {381},
  year         = {2021},
}

@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},
  pages        = {761–791},
  publisher    = {Springer Nature},
  title        = {{Complete gradient estimates of quantum Markov semigroups}},
  doi          = {10.1007/s00220-021-04199-4},
  volume       = {387},
  year         = {2021},
}

@article{8325,
  abstract     = {Let 𝐹:ℤ2→ℤ be the pointwise minimum of several linear functions. The theory of smoothing allows us to prove that under certain conditions there exists the pointwise minimal function among all integer-valued superharmonic functions coinciding with F “at infinity”. We develop such a theory to prove existence of so-called solitons (or strings) in a sandpile model, studied by S. Caracciolo, G. Paoletti, and A. Sportiello. Thus we made a step towards understanding the phenomena of the identity in the sandpile group for planar domains where solitons appear according to experiments. We prove that sandpile states, defined using our smoothing procedure, move changeless when we apply the wave operator (that is why we call them solitons), and can interact, forming triads and nodes. },
  author       = {Kalinin, Nikita and Shkolnikov, Mikhail},
  issn         = {1432-0916},
  journal      = {Communications in Mathematical Physics},
  number       = {9},
  pages        = {1649--1675},
  publisher    = {Springer Nature},
  title        = {{Sandpile solitons via smoothing of superharmonic functions}},
  doi          = {10.1007/s00220-020-03828-8},
  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{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         = {1432-0916},
  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         = {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{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{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},
}