@article{20045, abstract = {We consider the time evolution of the renormalized Nelson model, which describes N bosons linearly coupled to a quantized scalar field, in the mean-field limit of many particles N≫1 with coupling constant proportional to N^−1/2. First, we show that initial states exhibiting Bose–Einstein condensation for the particles and approximating a coherent state for the quantum field retain their structure under the many-body time evolution. Concretely, the dynamics of the reduced densities are approximated by solutions of two coupled PDEs, the Schrödinger–Klein–Gordon equations. Second, we construct a renormalized Bogoliubov evolution that describes the quantum fluctuations around the Schrödinger–Klein–Gordon equations. This evolution is used to extend the approximation of the evolved many-body state to the full norm topology. In summary, we provide a comprehensive analysis of the Nelson model that reveals the role of renormalization in the mean-field Bogoliubov theory.}, author = {Falconi, Marco and Lampart, Jonas and Leopold, Nikolai and Mitrouskas, David Johannes}, issn = {1873-1430}, journal = {Annales de l'Institut Henri Poincaré C}, publisher = {EMS Press}, title = {{Renormalized Bogoliubov theory for the Nelson model}}, doi = {10.4171/aihpc/154}, year = {2025}, } @article{20495, abstract = {We consider a tracer particle coupled to a Bose scalar field and study the regime where the field’s propagation speed approaches infinity. For initial states devoid of field excitations, we introduce an effective approximation of the time-evolved wave function and prove its validity in Hilbert space norm. In this approximation, the field remains in the vacuum state, while the tracer particle propagates with a modified dispersion relation. Physically, the new dispersion relation can be understood as the effect of radiative corrections due to interactions with virtual bosons. Mathematically, it is defined as the solution of a self-consistent nonlinear equation, whose form depends on the relevant time scale.}, author = {Cárdenas, Esteban and Mitrouskas, David Johannes}, issn = {1424-0637}, journal = {Annales Henri Poincare}, publisher = {Springer Nature}, title = {{Radiative corrections to the dynamics of a tracer particle coupled to a Bose ccalar field}}, doi = {10.1007/s00023-025-01626-3}, year = {2025}, } @article{19372, abstract = {We consider the confined Fröhlich polaron and establish an asymptotic series for the low-energy eigenvalues in negative powers of the coupling constant. The coefficients of the series are derived through a two-fold perturbation approach, involving expansions around the electron Pekar minimizer and the excitations of the quantum field.}, author = {Brooks, Morris and Mitrouskas, David Johannes}, issn = {2690-1005}, journal = {Probability and Mathematical Physics}, number = {1}, pages = {281--325}, publisher = {Mathematical Sciences Publishers}, title = {{ Asymptotic series for low-energy excitations of the Fröhlich polaron at strong coupling}}, doi = {10.2140/pmp.2025.6.281}, volume = {6}, year = {2025}, } @article{19660, abstract = {We analyze the ground state energy of N fermions in a two-dimensional box interacting with an impurity particle via two-body point interactions. We show that for weak coupling, the ground state energy is asymptotically described by the polaron energy, as proposed by F. Chevy in the physics literature. The polaron energy is the solution of a nonlinear equation involving the Green’s function of the free Fermi gas and the binding energy of the two-body point interaction. We provide quantitative error estimates that are uniform in the thermodynamic limit.}, author = {Mitrouskas, David Johannes}, issn = {1432-0673}, journal = {Archive for Rational Mechanics and Analysis}, number = {3}, publisher = {Springer Nature}, title = {{The weakly coupled two-dimensional Fermi polaron}}, doi = {10.1007/s00205-025-02098-9}, volume = {249}, year = {2025}, } @article{19661, abstract = {The Nelson model describes non-relativistic particles coupled to a relativistic Bose scalar field. In this article, we study the renormalized version of the Nelson model with massless bosons in Davies' weak coupling limit. Our main result states that the two-body Coulomb potential emerges as an effective pair interaction between the particles, which arises from the exchange of virtual excitations of the quantum field.}, author = {Cárdenas, Esteban and Mitrouskas, David Johannes}, issn = {1751-8121}, journal = {Journal of Physics A: Mathematical and Theoretical}, number = {17}, publisher = {IOP Publishing}, title = {{The renormalized Nelson model in the weak coupling limit}}, doi = {10.1088/1751-8121/adcdd9}, volume = {58}, year = {2025}, } @article{21270, abstract = {The one-dimensional Fröhlich model describing the motion of a single electron interacting with optical phonons is a paradigmatic model of quantum many-body physics. We predict the existence of an arbitrarily large number of bound excited states in the strong-coupling limit and calculate their excitation energies. Numerical simulations of a discretized model demonstrate the complete amelioration of the projector Monte Carlo sign problem by walker annihilation in an infinite Hilbert space. They reveal the threshold for the occurrence of the first bound excited states at a value of 𝛼≈1.73 for the dimensionless coupling constant. This puts the threshold into the regime of intermediate interaction strength. We find a significant spectral weight and increased phonon number of the bound excited state at threshold.}, author = {Taylor, J. and Čufar, M. and Mitrouskas, David Johannes and Seiringer, Robert and Pahl, E. and Brand, J.}, issn = {2469-9969}, journal = {Physical Review B}, number = {18}, publisher = {American Physical Society}, title = {{Bound excited states of Fröhlich polarons in one dimension}}, doi = {10.1103/s9p9-jflq}, volume = {112}, year = {2025}, } @inbook{18948, abstract = {We consider a gas of N bosons with interactions in the mean-field scaling regime. We review a recent proof of the asymptotic expansion of its spectrum and eigenstates and two applications of this result, namely the derivation of an Edgeworth expansion for fluctuations of one-body operators and the computation of the binding energy of an inhomogeneous Bose gas to any order. Finally, we collect related results for the dynamics of the weakly interacting Bose gas and for the regularized Nelson model.}, author = {Bossmann, Lea and Leopold, Nikolai and Mitrouskas, David Johannes and Petrat, Sören}, booktitle = {Physics and the Nature of Reality}, editor = {Bassi, Angelo and Goldstein, Sheldon and Tumulka, Roderich and Zanghi, Nino}, isbn = {9783031454332}, issn = {2365-6425}, pages = {307--321}, publisher = {Springer Nature}, title = {{Asymptotic Analysis of the Weakly Interacting Bose Gas: A Collection of Recent Results and Applications}}, doi = {10.1007/978-3-031-45434-9_22}, volume = {215}, year = {2024}, } @article{15318, abstract = {We consider a gas of N weakly interacting bosons in the ground state. Such gases exhibit Bose–Einstein condensation. The binding energy is defined as the energy it takes to remove one particle from the gas. In this article, we prove an asymptotic expansion for the binding energy, and compute the first orders explicitly for the homogeneous gas. Our result addresses in particular a conjecture by Nam (Lett Math Phys 108(1):141–159, 2018), and provides an asymptotic expansion of the ionization energy of bosonic atoms.}, author = {Bossmann, Lea and Leopold, Nikolai K and Mitrouskas, David Johannes and Petrat, Sören P}, issn = {1572-9613}, journal = {Journal of Statistical Physics}, number = {4}, publisher = {Springer Nature}, title = {{A note on the binding energy for Bosons in the mean-field limit}}, doi = {10.1007/s10955-024-03260-5}, volume = {191}, year = {2024}, } @article{14192, abstract = {For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the translation invariant Fröhlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling.}, author = {Lampart, Jonas and Mitrouskas, David Johannes and Mysliwy, Krzysztof}, issn = {1572-9656}, journal = {Mathematical Physics, Analysis and Geometry}, keywords = {Geometry and Topology, Mathematical Physics}, number = {3}, publisher = {Springer Nature}, title = {{On the global minimum of the energy–momentum relation for the polaron}}, doi = {10.1007/s11040-023-09460-x}, volume = {26}, year = {2023}, } @article{14715, abstract = {We consider N trapped bosons in the mean-field limit with coupling constant λN = 1/(N − 1). The ground state of such systems exhibits Bose–Einstein condensation. We prove that the probability of finding ℓ particles outside the condensate wave function decays exponentially in ℓ.}, author = {Mitrouskas, David Johannes and Pickl, Peter}, issn = {1089-7658}, journal = {Journal of Mathematical Physics}, number = {12}, publisher = {AIP Publishing}, title = {{Exponential decay of the number of excitations in the weakly interacting Bose gas}}, doi = {10.1063/5.0172199}, volume = {64}, year = {2023}, } @article{12430, abstract = {We study the time evolution of the Nelson model in a mean-field limit in which N nonrelativistic bosons weakly couple (with respect to the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body wave function in norm, with a convergence rate proportional to the number of corrections taken into account in the approximation. We prove an analogous result for the unitary propagator. As an application, we derive a simple system of partial differential equations describing the time evolution of the first- and second-order approximations to the one-particle reduced density matrices of the particles and the quantum field, respectively.}, author = {Falconi, Marco and Leopold, Nikolai K and Mitrouskas, David Johannes and Petrat, Sören P}, issn = {0129-055X}, journal = {Reviews in Mathematical Physics}, number = {4}, publisher = {World Scientific Publishing}, title = {{Bogoliubov dynamics and higher-order corrections for the regularized Nelson model}}, doi = {10.1142/S0129055X2350006X}, volume = {35}, year = {2023}, } @article{13178, abstract = {We consider the large polaron described by the Fröhlich Hamiltonian and study its energy-momentum relation defined as the lowest possible energy as a function of the total momentum. Using a suitable family of trial states, we derive an optimal parabolic upper bound for the energy-momentum relation in the limit of strong coupling. The upper bound consists of a momentum independent term that agrees with the predicted two-term expansion for the ground state energy of the strongly coupled polaron at rest and a term that is quadratic in the momentum with coefficient given by the inverse of twice the classical effective mass introduced by Landau and Pekar.}, author = {Mitrouskas, David Johannes and Mysliwy, Krzysztof and Seiringer, Robert}, issn = {2050-5094}, journal = {Forum of Mathematics}, pages = {1--52}, publisher = {Cambridge University Press}, title = {{Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron}}, doi = {10.1017/fms.2023.45}, volume = {11}, year = {2023}, } @article{14854, abstract = {We study the spectrum of the Fröhlich Hamiltonian for the polaron at fixed total momentum. We prove the existence of excited eigenvalues between the ground state energy and the essential spectrum at strong coupling. In fact, our main result shows that the number of excited energy bands diverges in the strong coupling limit. To prove this we derive upper bounds for the min-max values of the corresponding fiber Hamiltonians and compare them with the bottom of the essential spectrum, a lower bound on which was recently obtained by Brooks and Seiringer (Comm. Math. Phys. 404:1 (2023), 287–337). The upper bounds are given in terms of the ground state energy band shifted by momentum-independent excitation energies determined by an effective Hamiltonian of Bogoliubov type.}, author = {Mitrouskas, David Johannes and Seiringer, Robert}, issn = {2578-5885}, journal = {Pure and Applied Analysis}, keywords = {General Medicine}, number = {4}, pages = {973--1008}, publisher = {Mathematical Sciences Publishers}, title = {{Ubiquity of bound states for the strongly coupled polaron}}, doi = {10.2140/paa.2023.5.973}, volume = {5}, year = {2023}, } @article{14889, abstract = {We consider the Fröhlich Hamiltonian with large coupling constant α. For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding energy, we provide a norm approximation of the evolution, valid up to times of order α2. The approximation is given in terms of a Pekar product state, evolved through the Landau-Pekar equations, corrected by a Bogoliubov dynamics taking quantum fluctuations into account. This allows us to show that the Landau-Pekar equations approximately describe the evolution of the electron- and one-phonon reduced density matrices under the Fröhlich dynamics up to times of order α2.}, author = {Leopold, Nikolai K and Mitrouskas, David Johannes and Rademacher, Simone Anna Elvira and Schlein, Benjamin and Seiringer, Robert}, issn = {2578-5885}, journal = {Pure and Applied Analysis}, number = {4}, pages = {653--676}, publisher = {Mathematical Sciences Publishers}, title = {{Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron}}, doi = {10.2140/paa.2021.3.653}, volume = {3}, year = {2021}, } @article{9246, abstract = {We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.}, author = {Leopold, Nikolai K and Mitrouskas, David Johannes and Seiringer, Robert}, issn = {1432-0673}, journal = {Archive for Rational Mechanics and Analysis}, pages = {383--417}, publisher = {Springer Nature}, title = {{Derivation of the Landau–Pekar equations in a many-body mean-field limit}}, doi = {10.1007/s00205-021-01616-9}, volume = {240}, year = {2021}, } @article{9333, abstract = {We revise a previous result about the Fröhlich dynamics in the strong coupling limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter it was shown that the Fröhlich time evolution applied to the initial state φ0⊗ξα, where φ0 is the electron ground state of the Pekar energy functional and ξα the associated coherent state of the phonons, can be approximated by a global phase for times small compared to α2. In the present note we prove that a similar approximation holds for t=O(α2) if one includes a nontrivial effective dynamics for the phonons that is generated by an operator proportional to α−2 and quadratic in creation and annihilation operators. Our result implies that the electron ground state remains close to its initial state for times of order α2, while the phonon fluctuations around the coherent state ξα can be described by a time-dependent Bogoliubov transformation.}, author = {Mitrouskas, David Johannes}, issn = {1573-0530}, journal = {Letters in Mathematical Physics}, publisher = {Springer Nature}, title = {{A note on the Fröhlich dynamics in the strong coupling limit}}, doi = {10.1007/s11005-021-01380-7}, volume = {111}, year = {2021}, }