TY - JOUR AB - We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density šœŒ and inverse temperature š›½ differs from the one of the noninteracting system by the correction term šœ‹šœŒšœŒš›½š›½ . Here, is the scattering length of the interaction potential, and š›½ is the inverse Berezinskiiā€“Kosterlitzā€“Thouless critical temperature for superfluidity. The result is valid in the dilute limit šœŒ and if š›½šœŒ . AU - Deuchert, Andreas AU - Mayer, Simon AU - Seiringer, Robert ID - 7790 JF - Forum of Mathematics, Sigma TI - The free energy of the two-dimensional dilute Bose gas. I. Lower bound VL - 8 ER - TY - JOUR AB - We consider a dilute, homogeneous Bose gas at positive temperature. The system is investigated in the Grossā€“Pitaevskii limit, where the scattering length a is so small that the interaction energy is of the same order of magnitude as the spectral gap of the Laplacian, and for temperatures that are comparable to the critical temperature of the ideal gas. We show that the difference between the specific free energy of the interacting system and the one of the ideal gas is to leading order given by 4Ļ€a(2Ļ±2āˆ’Ļ±20). Here Ļ± denotes the density of the system and Ļ±0 is the expected condensate density of the ideal gas. Additionally, we show that the one-particle density matrix of any approximate minimizer of the Gibbs free energy functional is to leading order given by the one of the ideal gas. This in particular proves Boseā€“Einstein condensation with critical temperature given by the one of the ideal gas to leading order. One key ingredient of our proof is a novel use of the Gibbs variational principle that goes hand in hand with the c-number substitution. AU - Deuchert, Andreas AU - Seiringer, Robert ID - 7650 IS - 6 JF - Archive for Rational Mechanics and Analysis SN - 0003-9527 TI - Gross-Pitaevskii limit of a homogeneous Bose gas at positive temperature VL - 236 ER - TY - JOUR AB - Inspired by the possibility to experimentally manipulate and enhance chemical reactivity in helium nanodroplets, we investigate the effective interaction and the resulting correlations between two diatomic molecules immersed in a bath of bosons. By analogy with the bipolaron, we introduce the biangulon quasiparticle describing two rotating molecules that align with respect to each other due to the effective attractive interaction mediated by the excitations of the bath. We study this system in different parameter regimes and apply several theoretical approaches to describe its properties. Using a Bornā€“Oppenheimer approximation, we investigate the dependence of the effective intermolecular interaction on the rotational state of the two molecules. In the strong-coupling regime, a product-state ansatz shows that the molecules tend to have a strong alignment in the ground state. To investigate the system in the weak-coupling regime, we apply a one-phonon excitation variational ansatz, which allows us to access the energy spectrum. In comparison to the angulon quasiparticle, the biangulon shows shifted angulon instabilities and an additional spectral instability, where resonant angular momentum transfer between the molecules and the bath takes place. These features are proposed as an experimentally observable signature for the formation of the biangulon quasiparticle. Finally, by using products of single angulon and bare impurity wave functions as basis states, we introduce a diagonalization scheme that allows us to describe the transition from two separated angulons to a biangulon as a function of the distance between the two molecules. AU - Li, Xiang AU - Yakaboylu, Enderalp AU - Bighin, Giacomo AU - Schmidt, Richard AU - Lemeshko, Mikhail AU - Deuchert, Andreas ID - 8587 IS - 16 JF - The Journal of Chemical Physics KW - Physical and Theoretical Chemistry KW - General Physics and Astronomy SN - 0021-9606 TI - Intermolecular forces and correlations mediated by a phonon bath VL - 152 ER - TY - JOUR AB - We consider an interacting, dilute Bose gas trapped in a harmonic potential at a positive temperature. The system is analyzed in a combination of a thermodynamic and a Grossā€“Pitaevskii (GP) limit where the trap frequency Ļ‰, the temperature T, and the particle number N are related by Nāˆ¼ (T/ Ļ‰) 3ā†’ āˆž while the scattering length is so small that the interaction energy per particle around the center of the trap is of the same order of magnitude as the spectral gap in the trap. We prove that the difference between the canonical free energy of the interacting gas and the one of the noninteracting system can be obtained by minimizing the GP energy functional. We also prove Boseā€“Einstein condensation in the following sense: The one-particle density matrix of any approximate minimizer of the canonical free energy functional is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the GP minimizer. AU - Deuchert, Andreas AU - Seiringer, Robert AU - Yngvason, Jakob ID - 80 IS - 2 JF - Communications in Mathematical Physics TI - Boseā€“Einstein condensation in a dilute, trapped gas at positive temperature VL - 368 ER - TY - GEN AB - We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\rho$ and inverse temperature $\beta$ differs from the one of the non-interacting system by the correction term $4 \pi \rho^2 |\ln a^2 \rho|^{-1} (2 - [1 - \beta_{\mathrm{c}}/\beta]_+^2)$. Here $a$ is the scattering length of the interaction potential, $[\cdot]_+ = \max\{ 0, \cdot \}$ and $\beta_{\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless critical temperature for superfluidity. The result is valid in the dilute limit $a^2\rho \ll 1$ and if $\beta \rho \gtrsim 1$. AU - Deuchert, Andreas AU - Mayer, Simon AU - Seiringer, Robert ID - 7524 T2 - arXiv:1910.03372 TI - The free energy of the two-dimensional dilute Bose gas. I. Lower bound ER - TY - JOUR AB - We consider the two-dimensional BCS functional with a radial pair interaction. We show that the translational symmetry is not broken in a certain temperature interval below the critical temperature. In the case of vanishing angular momentum, our results carry over to the three-dimensional case. AU - Deuchert, Andreas AU - Geisinge, Alissa AU - Hainzl, Christian AU - Loss, Michael ID - 400 IS - 5 JF - Annales Henri Poincare TI - Persistence of translational symmetry in the BCS model with radial pair interaction VL - 19 ER - TY - JOUR AB - We study a quantum impurity possessing both translational and internal rotational degrees of freedom interacting with a bosonic bath. Such a system corresponds to a ā€œrotating polaron,ā€ which can be used to model, e.g., a rotating molecule immersed in an ultracold Bose gas or superfluid helium. We derive the Hamiltonian of the rotating polaron and study its spectrum in the weak- and strong-coupling regimes using a combination of variational, diagrammatic, and mean-field approaches. We reveal how the coupling between linear and angular momenta affects stable quasiparticle states, and demonstrate that internal rotation leads to an enhanced self-localization in the translational degrees of freedom. AU - Yakaboylu, Enderalp AU - Midya, Bikashkali AU - Deuchert, Andreas AU - Leopold, Nikolai K AU - Lemeshko, Mikhail ID - 5983 IS - 22 JF - Physical Review B SN - 2469-9950 TI - Theory of the rotating polaron: Spectrum and self-localization VL - 98 ER - TY - JOUR AB - Recently it was shown that molecules rotating in superfluid helium can be described in terms of the angulon quasiparticles (Phys. Rev. Lett. 118, 095301 (2017)). Here we demonstrate that in the experimentally realized regime the angulon can be seen as a point charge on a 2-sphere interacting with a gauge field of a non-abelian magnetic monopole. Unlike in several other settings, the gauge fields of the angulon problem emerge in the real coordinate space, as opposed to the momentum space or some effective parameter space. Furthermore, we find a topological transition associated with making the monopole abelian, which takes place in the vicinity of the previously reported angulon instabilities. These results pave the way for studying topological phenomena in experiments on molecules trapped in superfluid helium nanodroplets, as well as on other realizations of orbital impurity problems. AU - Yakaboylu, Enderalp AU - Deuchert, Andreas AU - Lemeshko, Mikhail ID - 997 IS - 23 JF - Physical Review Letters SN - 0031-9007 TI - Emergence of non-abelian magnetic monopoles in a quantum impurity problem VL - 119 ER - TY - JOUR AB - We consider a many-body system of fermionic atoms interacting via a local pair potential and subject to an external potential within the framework of Bardeen-Cooper-Schrieffer (BCS) theory. We measure the free energy of the whole sample with respect to the free energy of a reference state which allows us to define a BCS functional with boundary conditions at infinity. Our main result is a lower bound for this energy functional in terms of expressions that typically appear in Ginzburg-Landau functionals. AU - Deuchert, Andreas ID - 912 IS - 8 JF - Journal of Mathematical Physics SN - 00222488 TI - A lower bound for the BCS functional with boundary conditions at infinity VL - 58 ER -