[{"day":"01","publication_status":"published","title":"Scaling limits of Schrödinger quantum mechanics","alternative_title":["LNP"],"abstract":[{"lang":"eng","text":"We outline the status of rigorous derivations of certain classical evolution equations as limits of Schrödinger dynamics. We explain two recent results jointly with H.T. Yau in more details. The first one is the derivation of the linear Boltzmann equation as the long time limit of the one-body Schrödinger equation with a random potential. The second one is the mean field limit of high density bosons with Coulomb interaction that leads to the nonlinear Hartree equation."}],"date_updated":"2021-01-12T06:59:06Z","date_created":"2018-12-11T11:59:06Z","citation":{"chicago":"Erdös, László. “Scaling Limits of Schrödinger Quantum Mechanics,” 597:487–506. Springer, 2002. https://doi.org/10.1007/3-540-46122-1_19.","ama":"Erdös L. Scaling limits of Schrödinger quantum mechanics. In: Vol 597. Springer; 2002:487-506. doi:10.1007/3-540-46122-1_19","ista":"Erdös L. 2002. Scaling limits of Schrödinger quantum mechanics. 38th Winter School of Theoretical Physics : Dynamical Semigroups: Dissipation, Chaos, Quanta, LNP, vol. 597, 487–506.","apa":"Erdös, L. (2002). Scaling limits of Schrödinger quantum mechanics (Vol. 597, pp. 487–506). Presented at the 38th Winter School of Theoretical Physics : Dynamical Semigroups: Dissipation, Chaos, Quanta, Springer. https://doi.org/10.1007/3-540-46122-1_19","ieee":"L. Erdös, “Scaling limits of Schrödinger quantum mechanics,” presented at the 38th Winter School of Theoretical Physics : Dynamical Semigroups: Dissipation, Chaos, Quanta, 2002, vol. 597, pp. 487–506.","short":"L. Erdös, in:, Springer, 2002, pp. 487–506.","mla":"Erdös, László. *Scaling Limits of Schrödinger Quantum Mechanics*. Vol. 597, Springer, 2002, pp. 487–506, doi:10.1007/3-540-46122-1_19."},"_id":"2694","publisher":"Springer","date_published":"2002-01-01T00:00:00Z","conference":{"name":"38th Winter School of Theoretical Physics : Dynamical Semigroups: Dissipation, Chaos, Quanta"},"volume":597,"year":"2002","intvolume":" 597","extern":1,"type":"conference","author":[{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"László Erdös"}],"status":"public","publist_id":"4203","doi":"10.1007/3-540-46122-1_19","quality_controlled":0,"page":"487 - 506","month":"01"},{"date_created":"2018-12-11T11:59:11Z","citation":{"chicago":"Erdös, László. “Two Dimensional Pauli Operator via Scalar Potential,” 307:129–33. World Scientific Publishing, 2002. https://doi.org/10.1090/conm/307.","ista":"Erdös L. 2002. Two dimensional Pauli operator via scalar potential. QMath: Mathematical Results in Quantum Physics, Contemporary Mathematics, vol. 307, 129–133.","ama":"Erdös L. Two dimensional Pauli operator via scalar potential. In: Vol 307. World Scientific Publishing; 2002:129-133. doi:10.1090/conm/307","apa":"Erdös, L. (2002). Two dimensional Pauli operator via scalar potential (Vol. 307, pp. 129–133). Presented at the QMath: Mathematical Results in Quantum Physics, World Scientific Publishing. https://doi.org/10.1090/conm/307","ieee":"L. Erdös, “Two dimensional Pauli operator via scalar potential,” presented at the QMath: Mathematical Results in Quantum Physics, 2002, vol. 307, pp. 129–133.","short":"L. Erdös, in:, World Scientific Publishing, 2002, pp. 129–133.","mla":"Erdös, László. *Two Dimensional Pauli Operator via Scalar Potential*. Vol. 307, World Scientific Publishing, 2002, pp. 129–33, doi:10.1090/conm/307."},"date_updated":"2021-01-12T06:59:11Z","alternative_title":["Contemporary Mathematics"],"title":"Two dimensional Pauli operator via scalar potential","publication_status":"published","day":"01","month":"01","page":"129 - 133","publist_id":"4188","quality_controlled":0,"doi":"10.1090/conm/307","author":[{"full_name":"László Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"}],"status":"public","intvolume":" 307","extern":1,"type":"conference","volume":307,"year":"2002","conference":{"name":"QMath: Mathematical Results in Quantum Physics"},"_id":"2708","publisher":"World Scientific Publishing","date_published":"2002-01-01T00:00:00Z"},{"page":"515 - 520","month":"03","author":[{"last_name":"Bardos","first_name":"Claude","full_name":"Bardos, Claude"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"László Erdös"},{"first_name":"François","last_name":"Golse","full_name":"Golse, François"},{"last_name":"Mauser","first_name":"Norbert","full_name":"Mauser, Norbert J"},{"first_name":"Horng","last_name":"Yau","full_name":"Yau, Horng-Tzer"}],"status":"public","publist_id":"4155","doi":"10.1016/S1631-073X(02)02253-7","quality_controlled":0,"volume":334,"year":"2002","intvolume":" 334","extern":1,"type":"journal_article","_id":"2737","issue":"6","date_published":"2002-03-30T00:00:00Z","publisher":"Elsevier","publication":"Comptes Rendus Mathematique","abstract":[{"lang":"eng","text":"We derive the time-dependent Schrödinger–Poisson equation as the weak coupling limit of the N-body linear Schrödinger equation with Coulomb potential."}],"date_updated":"2021-01-12T06:59:22Z","date_created":"2018-12-11T11:59:20Z","citation":{"ista":"Bardos C, Erdös L, Golse F, Mauser N, Yau H. 2002. Derivation of the Schrödinger-Poisson equation from the quantum N-body problem. Comptes Rendus Mathematique. 334(6), 515–520.","ama":"Bardos C, Erdös L, Golse F, Mauser N, Yau H. Derivation of the Schrödinger-Poisson equation from the quantum N-body problem. *Comptes Rendus Mathematique*. 2002;334(6):515-520. doi:10.1016/S1631-073X(02)02253-7","apa":"Bardos, C., Erdös, L., Golse, F., Mauser, N., & Yau, H. (2002). Derivation of the Schrödinger-Poisson equation from the quantum N-body problem. *Comptes Rendus Mathematique*. Elsevier. https://doi.org/10.1016/S1631-073X(02)02253-7","chicago":"Bardos, Claude, László Erdös, François Golse, Norbert Mauser, and Horng Yau. “Derivation of the Schrödinger-Poisson Equation from the Quantum N-Body Problem.” *Comptes Rendus Mathematique*. Elsevier, 2002. https://doi.org/10.1016/S1631-073X(02)02253-7.","mla":"Bardos, Claude, et al. “Derivation of the Schrödinger-Poisson Equation from the Quantum N-Body Problem.” *Comptes Rendus Mathematique*, vol. 334, no. 6, Elsevier, 2002, pp. 515–20, doi:10.1016/S1631-073X(02)02253-7.","ieee":"C. Bardos, L. Erdös, F. Golse, N. Mauser, and H. Yau, “Derivation of the Schrödinger-Poisson equation from the quantum N-body problem,” *Comptes Rendus Mathematique*, vol. 334, no. 6. Elsevier, pp. 515–520, 2002.","short":"C. Bardos, L. Erdös, F. Golse, N. Mauser, H. Yau, Comptes Rendus Mathematique 334 (2002) 515–520."},"publication_status":"published","title":"Derivation of the Schrödinger-Poisson equation from the quantum N-body problem","day":"30"},{"volume":107,"year":"2002","intvolume":" 107","type":"journal_article","extern":1,"_id":"2738","date_published":"2002-06-01T00:00:00Z","publisher":"Springer","publication":"Journal of Statistical Physics","issue":"5-6","page":"1043 - 1127","month":"06","author":[{"orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"László Erdös"}],"status":"public","publist_id":"4154","doi":"10.1023/A:1015157624384","quality_controlled":0,"publication_status":"published","title":"Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field","day":"01","abstract":[{"lang":"eng","text":"We consider the long time evolution of a quantum particle weakly interacting with a phonon field. We show that in the weak coupling limit the Wigner distribution of the electron density matrix converges to the solution of the linear Boltzmann equation globally in time. The collision kernel is identified as the sum of an emission and an absorption term that depend on the equilibrium distribution of the free phonon modes."}],"date_updated":"2021-01-12T06:59:22Z","date_created":"2018-12-11T11:59:20Z","citation":{"chicago":"Erdös, László. “Linear Boltzmann Equation as the Long Time Dynamics of an Electron Weakly Coupled to a Phonon Field.” *Journal of Statistical Physics*. Springer, 2002. https://doi.org/10.1023/A:1015157624384.","ista":"Erdös L. 2002. Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. Journal of Statistical Physics. 107(5–6), 1043–1127.","ama":"Erdös L. Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. *Journal of Statistical Physics*. 2002;107(5-6):1043-1127. doi:10.1023/A:1015157624384","apa":"Erdös, L. (2002). Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field. *Journal of Statistical Physics*. Springer. https://doi.org/10.1023/A:1015157624384","ieee":"L. Erdös, “Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field,” *Journal of Statistical Physics*, vol. 107, no. 5–6. Springer, pp. 1043–1127, 2002.","short":"L. Erdös, Journal of Statistical Physics 107 (2002) 1043–1127.","mla":"Erdös, László. “Linear Boltzmann Equation as the Long Time Dynamics of an Electron Weakly Coupled to a Phonon Field.” *Journal of Statistical Physics*, vol. 107, no. 5–6, Springer, 2002, pp. 1043–127, doi:10.1023/A:1015157624384."}},{"status":"public","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"László Erdös"},{"full_name":"Vougalter, Vitali","last_name":"Vougalter","first_name":"Vitali"}],"quality_controlled":0,"doi":"10.1007/s002200100585","publist_id":"4153","page":"399 - 421","month":"02","date_published":"2002-02-01T00:00:00Z","publication":"Communications in Mathematical Physics","publisher":"Springer","issue":"2","_id":"2739","year":"2002","volume":225,"extern":1,"type":"journal_article","intvolume":" 225","date_updated":"2021-01-12T06:59:23Z","abstract":[{"text":"We define the two dimensional Pauli operator and identify its core for magnetic fields that are regular Borel measures. The magnetic field is generated by a scalar potential hence we bypass the usual A L 2loc condition on the vector potential, which does not allow to consider such singular fields. We extend the Aharonov-Casher theorem for magnetic fields that are measures with finite total variation and we present a counterexample in case of infinite total variation. One of the key technical tools is a weighted L 2 estimate on a singular integral operator.","lang":"eng"}],"citation":{"mla":"Erdös, László, and Vitali Vougalter. “Pauli Operator and Aharonov-Casher Theorem for Measure Valued Magnetic Fields.” *Communications in Mathematical Physics*, vol. 225, no. 2, Springer, 2002, pp. 399–421, doi:10.1007/s002200100585.","short":"L. Erdös, V. Vougalter, Communications in Mathematical Physics 225 (2002) 399–421.","ieee":"L. Erdös and V. Vougalter, “Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields,” *Communications in Mathematical Physics*, vol. 225, no. 2. Springer, pp. 399–421, 2002.","apa":"Erdös, L., & Vougalter, V. (2002). Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields. *Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s002200100585","ista":"Erdös L, Vougalter V. 2002. Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields. Communications in Mathematical Physics. 225(2), 399–421.","ama":"Erdös L, Vougalter V. Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields. *Communications in Mathematical Physics*. 2002;225(2):399-421. doi:10.1007/s002200100585","chicago":"Erdös, László, and Vitali Vougalter. “Pauli Operator and Aharonov-Casher Theorem for Measure Valued Magnetic Fields.” *Communications in Mathematical Physics*. Springer, 2002. https://doi.org/10.1007/s002200100585."},"date_created":"2018-12-11T11:59:21Z","day":"01","publication_status":"published","title":"Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields"}]