Publications

Preprints

  1. Zi-Xiang Li, Abolhassan Vaezi, Christian B. Mendl, Hong Yao
    Emergent spacetime supersymmetry at superconducting quantum criticality of single Dirac cone (arXiv:1711.04772)
  2. Edwin W. Huang, Christian B. Mendl, Hong-Chen Jiang, Brian Moritz, Thomas P. Devereaux
    Stripe order from the perspective of the Hubbard model (arXiv:1709.02398)
  3. Chunjing J. Jia, Yao Wang, Christian B. Mendl, Brian Moritz, Thomas P. Devereaux
    Paradeisos: a perfect hashing algorithm for many-body eigenvalue problems (arXiv:1707.03974)
  4. Christian B. Mendl, Silvia Palpacelli, Alex Kamenev, Sauro Succi
    Quantum lattice Boltzmann study of random-mass Dirac fermions in one dimension (arXiv:1706.05138)

Peer reviewed papers

2017

  1. stripes Edwin W. Huang, Christian B. Mendl, Shenxiu Liu, Steven Johnston, Hong-Chen Jiang, Brian Moritz, Thomas P. Devereaux
    Numerical evidence of fluctuating stripes in the normal state of high-Tc cuprate superconductors [pdf]
    Science 358, 1161-1164 (2017) [doi], (arXiv:1612.05211)
    Together with Edwin, I implemented the "Determinant quantum Monte Carlo" code (C with Intel MKL) used for the computations in the paper, available at GitHub. See also the news announcement at SLAC.
  2. Christian B. Mendl, Elizabeth A. Nowadnick, Edwin W. Huang, Steven Johnston, Brian Moritz, Thomas P. Devereaux
    Doping dependence of ordered phases and emergent quasiparticles in the doped Hubbard-Holstein model [pdf]
    Phys. Rev. B 96, 205141 (2017) [doi], (arXiv:1709.00245)
  3. Annabelle Bohrdt, Christian B. Mendl, Manuel Endres, Michael Knap
    Scrambling and thermalization in a diffusive quantum many-body system [pdf]
    New J. Phys. 19, 063001 (2017) [doi], (arXiv:1612.02434)
    I implemented and ran the numerical simulations in the paper, based on matrix product operators (MPOs). The source code is available at GitHub.
  4. Christian B. Mendl, Herbert Spohn
    Shocks, rarefaction waves, and current fluctuations for anharmonic chains [pdf]
    J. Stat. Phys. 166, 841-875 (2017) [doi], (arXiv:1607.05205)
    Detailed derivations related to the publication "Searching for the Tracy-Widom distribution in nonequilibrium processes" below.

2016

  1. Christian B. Mendl, Jianfeng Lu, Jani Lukkarinen
    Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory [pdf]
    Phys. Rev. E 94, 062104 (2016) [doi], (arXiv:1608.08308)
    Using Wigner functions derived from kinetic theory to study thermalization. Motivated by the active research field "thermalization of isolated quantum systems".
  2. Christian B. Mendl, Herbert Spohn
    Searching for the Tracy-Widom distribution in nonequilibrium processes [pdf]
    Phys. Rev. E 93, 060101(R) (2016) [doi], (arXiv:1512.06292)
    The height fluctuations for one-dimensional growth models in the Kardar-Parisi-Zhang universality class are governed by the random matrix Tracy-Widom distribution. Here we demonstrate that the Tracy-Widom distribution also occurs for the Leroux stochastic lattice gas and hard-point particle chains with alternating masses, when starting from domain wall initial conditions. The result is expected to be general, and should also hold for other anharmonic chains and one-dimensional quantum fluids.
  3. Christian B. Mendl
    Efficient algorithm for many-electron angular momentum and spin diagonalization on atomic subshells [pdf]
    Commun. Comput. Phys. 19, 192-204 (2016) [doi], (arXiv:1409.6860)
    A Mathematica implementation of the algorithm described in the paper is available at GitHub. The algorithm is an improved version of the LS diagonalization step used in the paper "Efficient algorithm for asymptotics-based configuration-interaction methods and electronic structure of transition metal atoms" below.

2015

  1. Christian B. Mendl, Herbert Spohn
    Low temperature dynamics of the one-dimensional discrete nonlinear Schrödinger equation [pdf]
    J. Stat. Mech. (2015) P08028 [doi], (arXiv:1505.04218)
    Nonlinear fluctuating hydrodynamics applied to the discrete nonlinear Schrödinger equation. At low temperatures, the "superfluid velocity" is almost conserved, which opens a "second sound" transportation channel.
  2. Francesc Malet, André Mirtschink, Christian B. Mendl, Johannes Bjerlin, Elife Ö. Karabulut, Stephanie M. Reimann, Paola Gori-Giorgi
    Density functional theory for strongly-correlated bosonic and fermionic ultracold dipolar and ionic gases [pdf]
    Phys. Rev. Lett. 115, 033006 (2015) [doi], (arXiv:1502.01469)
    An alternative functional for DFT calculations enables simulations of ultracold gases with long-ranged interactions. Also refer to the paper "Wigner localization in quantum dots from Kohn-Sham density functional theory without symmetry breaking" below.
  3. Jianfeng Lu, Christian B. Mendl
    Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation [pdf]
    J. Comput. Phys. 291, 303-316 (2015) [doi], (arXiv:1408.1782)
    Development and implementation of an efficient algorithm for the spatially inhomogeneous matrix-valued quantum Boltzmann equation derived from the Hubbard model. Also compare with the Boltzmann-Hubbard papers below concerned with the one-dimensional case.
  4. Christian B. Mendl, Herbert Spohn
    Current fluctuations for anharmonic chains in thermal equilibrium [pdf]
    J. Stat. Mech. (2015) P03007 [doi], (arXiv:1412.4609)
    The C source code for the simulations can be found at here, and a Mathematica package and demonstration file for calculating the G coupling constants here. See also the papers "Equilibrium time-correlation functions for one-dimensional hard-point systems" and "Dynamic correlators of Fermi-Pasta-Ulam chains and nonlinear fluctuating hydrodynamics" below.
  5. Christian B. Mendl
    Matrix-valued quantum lattice Boltzmann method [pdf]
    Int. J. Mod. Phys. C 26, 1550113 (2015) [doi], (arXiv:1309.1656)
    Lattice Boltzmann method (LBM) with quantum aspects: Fermi-Dirac equilibrium functions instead of Maxwell-Boltzmann, and matrix-valued spin density matrices as distribution functions. See also the video in the software section.
  6. Martin L.R. Fürst, Markus Kotulla, Christian B. Mendl, Herbert Spohn
    Quantum Boltzmann equation for spin-dependent reactions in the kinetic regime [pdf]
    J. Phys. A 48, 095204 (2015) [doi], (arXiv:1411.2576)
    Matrix-valued multi-component Boltzmann equation derived from a general quantum field Hamiltonian. We illustrate the approach to equilibrium by numerical simulations in the isotropic three-dimensional setting.

2014

  1. Huajie Chen, Gero Friesecke, Christian B. Mendl
    Numerical methods for a Kohn-Sham density functional model based on optimal transport [pdf]
    J. Chem. Theory Comput. 10, 4360-4368 (2014) [doi], (arXiv:1405.7026)
    Finite element discretization of the optimal transport map for N = 2 electrons.
  2. Christian B. Mendl, Herbert Spohn
    Equilibrium time-correlation functions for one-dimensional hard-point systems [pdf]
    Phys. Rev. E 90, 012147 (2014) [doi], (arXiv:1403.0213)
    Comparing molecular dynamics simulations of hard-point chains with predictions from nonlinear fluctuating hydrodynamics. A slightly improved version of the C source code used for the simulations can be found here, and a Mathematica package and demonstration file for calculating the G coupling constants here. See also the PRL "Dynamic correlators of Fermi-Pasta-Ulam chains and nonlinear fluctuating hydrodynamics" below and the paper by Herbert Spohn "Nonlinear fluctuating hydrodynamics for anharmonic chains", J. Stat. Phys. 154, 1191-1227 (2014).
  3. Suman G. Das, Abhishek Dhar, Keiji Saito, Christian B. Mendl, Herbert Spohn
    Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain [pdf]
    Phys. Rev. E 90, 012124 (2014) [doi], (arXiv:1404.7081)
  4. Martin L.R. Fürst, Christian B. Mendl, Herbert Spohn
    Dynamics of the Bose-Hubbard chain for weak interactions [pdf]
    Phys. Rev. B 89, 134311 (2014) [doi], (arXiv:1312.6737)
    Matrix-valued Boltzmann equation for the Bose-Hubbard chain in the kinetic regime, including a theoretical derivation and numerical simulations. Concerning the Fermi-Hubbard chain, see the papers below.
  5. Christian B. Mendl, Francesc Malet, Paola Gori-Giorgi
    Wigner localization in quantum dots from Kohn-Sham density functional theory without symmetry breaking [pdf]
    Phys. Rev. B 89, 125106 (2014) [doi], (arXiv:1311.6011)
    Kohn-Sham DFT calculations with the SCE functional, implemented using C and Mathematica. A slightly improved version of the C source code and a Mathematica demonstration file can be found at GitHub.

2013

  1. Christian B. Mendl, Herbert Spohn
    Dynamic correlators of Fermi-Pasta-Ulam chains and nonlinear fluctuating hydrodynamics [pdf]
    Phys. Rev. Lett. 111, 230601 (2013) [doi], (arXiv:1305.1209)
    For the underlying theory of nonlinear fluctuating hydrodynamics for anharmonic chains, refer to arXiv:1305.6412. A Mathematica package and demonstration file for calculating the coupling constants can be found at GitHub.
  2. Gero Friesecke, Christian B. Mendl, Brendan Pass, Codina Cotar, Claudia Klüppelberg
    N-density representability and the optimal transport limit of the Hohenberg-Kohn functional [pdf]
    J. Chem. Phys. 139, 164109 (2013) [doi], (arXiv:1304.0679)
    Similar topic as in "Kantorovich dual solution for strictly correlated electrons in atoms and molecules". I'm responsible for the calculations involving small atoms in the paper.
  3. Martin L.R. Fürst, Christian B. Mendl, Herbert Spohn
    Matrix-valued Boltzmann equation for the nonintegrable Hubbard chain [pdf]
    Phys. Rev. E 88, 012108 (2013) [doi], (arXiv:1302.2075)
    Follow-up paper for the non-integrable case. I am mainly responsible for the numeric part, which requires more sophistication than the integrable case to adopt the conservation laws in the numeric discretization. The (slightly improved) C / Mathematica source code for the simulations can be found at GitHub.
  4. Christian B. Mendl, Lin Lin
    Kantorovich dual solution for strictly correlated electrons in atoms and molecules [pdf]
    Phys. Rev. B 87, 125106 (2013) [doi], (arXiv:1210.7117)
    We develop a nested optimization method to solve the Kantorovich dual formulation of optimal transport directly, with applications to atoms and small molecules.
  5. Christian B. Mendl, Steven Eliuk, Michelle Noga, and Pierre Boulanger
    Comprehensive analysis of high-performance computing methods for filtered back-projection [pdf]
    ELCVIA 12(1): 1-16 (2013) [journal link].
    Based on the Radon transform implementation in the software section, but for fan-beam geometry.

2012

  1. Martin L.R. Fürst, Christian B. Mendl, Herbert Spohn
    Matrix-valued Boltzmann equation for the Hubbard chain [pdf]
    Phys. Rev. E 86, 031122 (2012) [doi], (arXiv:1207.6926)
    The time-dependent Wigner function is matrix-valued due to spin.
  2. Christian B. Mendl
    Efficient algorithm for two-center Coulomb and exchange integrals of electronic prolate spheroidal orbitals [pdf]
    J. Comput. Phys. 231, 5157-5175 (2012) [doi], (arXiv:1203.6256)
    The paper presents a fast algorithm to calculate Coulomb/exchange integrals of prolate spheroidal electronic orbitals, which appear in di-atomic molecules. The Mathematica code used for the calculations in the paper is available at GitHub.

2011

  1. Christian B. Mendl
    The FermiFab toolbox for fermionic many-particle quantum systems [pdf]
    Comput. Phys. Commun. 182, 1327-1337 (2011) [doi], (arXiv:1103.0872)
    This paper descibes the FermiFab Matlab and Mathematica toolbox (available at SourceForge), focusing on the implementation details based on integer bitfields.

2010

  1. Christian B. Mendl, Gero Friesecke
    Efficient algorithm for asymptotics-based configuration-interaction methods and electronic structure of transition metal atoms [pdf]
    J. Chem. Phys. 133, 184101 (2010) [doi], (arXiv:1009.2013)
    Several Mathematica notebooks used for the calculations are available here: [zip]. The FermiFab toolbox (also see above paper) has originally been developed to perform the symbolic and numerical calculations described in this paper.

2009

  1. Birkhoff Christian B. Mendl, Michael M. Wolf
    Unital quantum channels - Convex structure and revivals of Birkhoff's theorem [pdf]
    Commun. Math. Phys. 289, 1057-1086 (2009) [doi], (arXiv:0806.2820)
    Basically a compact version of my physics diploma thesis.

Conference proceedings

  1. Christian B. Mendl (joint with Michael Knap, Johannes M. Oberreuter, Herbert Spohn)
    Nonequilibrium dynamics of the Bose-Hubbard model and discrete nonlinear Schrödinger equation in one dimension [pdf] [link]
    APS March Meeting 2017, New Orleans, USA
  2. Christian B. Mendl (joint with Elizabeth Nowadnick, Yvonne Kung, Brian Moritz, Steven Johnston, Thomas Devereaux)
    Doping dependence of ordered phases in the Hubbard-Holstein model [pdf] [link]
    APS March Meeting 2016, Baltimore, USA
  3. Tim Gollisch, Vidhyasankar Krishnamoorthy, Christian B. Mendl
    Neural encoding of saccadic stimuli in the retina [pdf]
    Tenth International Neural Coding Workshop Prague, Czech Republic (2012)
  4. Christian B. Mendl (joint with Gero Friesecke)
    Electronic structure of 3d transition metal atoms [pdf]
    Oberwolfach Reports 8 (2011), issue 2, pp. 1769-1843 [doi]
    Mathematical Methods in Quantum Chemistry

Diploma Theses

Physics

MPQ
Diploma Thesis: Unital quantum channels [pdf]
(June 2008, 60 pages)
Advisors: Prof. Dr. J. Ignacio Cirac
Prof. Dr. Michael M. Wolf
Address: Theory Division
Max-Planck-Institut für Quantenoptik
Hans-Kopfermann-Straße 1
D-85748 Garching bei München

Mathematics

Mathematics Department
Diploma Thesis: The N-representability problem and
orbital occupation in transition metals
[pdf]
(July 2008, 58 pages)
Bachelor Thesis: The representability problem in many-body quantum mechanics [pdf]
(October 2006, 32 pages)
Advisor: Prof. PhD. Gero Friesecke
Address: Department of Mathematics - Global Analysis
Technische Universität München
Boltzmannstraße 3
D-85747 Garching bei München

PhD Statistical (Bio-)Physics

I've completed my PhD at the Ludwig-Maximilians-Universität München, supervised by Prof. Dr. Tim Gollisch and Prof. Dr. Erwin Frey. Experimental work was performed at the Max-Planck-Institute of Neurobiology, München. (The Gollisch group has moved to Göttingen in the meantime.)
PhD Thesis: Neuronal coding in the retina: Effects of
eye movements and network interactions
[pdf] [link]
(7. December 2011, 128 pages)
Advisors: Prof. Dr. Tim Gollisch
Prof. Dr. Erwin Frey
Scholarship: Boehringer Ingelheim Fonds PhD Fellowship

Selected Talks and Notes

Matrix-valued Quantum Boltzmann Methods [pdf] (November 2016).
Talk at the KI-Net Young Researchers Workshop: Stochastic and deterministic methods in kinetic theory, Duke University, USA.

Searching for the Tracy-Widom Distribution in Nonequilibrium Processes [pdf] (October 2016).
Talk at the Mathematical Physics and Probability seminar, UC Davis, USA.

Determinant quantum Monte Carlo algorithm for simulating Hubbard models [pdf] (July 2016).
Talk at the workshop "Mathematical and numerical analysis of electronic structure models", Roscoff, France.

Doping dependence of ordered phases in the Hubbard-Holstein model [pdf] (March 2016).
Talk at the APS March meeting 2016, Baltimore, USA.

Low temperature dynamics of the one-dimensional discrete nonlinear Schrödinger equation [pdf] (February 2016).
Talk at the workshop "New approaches to non-equilibrium and random systems", KITP, UC Santa Barbara, USA.

Kohn-Sham density functional theory in the framework of "strictly correlated electrons" [zip] (April 2014).
Talk at the "Workshop on Mathematical and numerical analysis of electronic structure models", Konrad-Zuse Institut Berlin, Germany.

Optimal transport limit of the Hohenberg-Kohn functional: Kantorovich dual solution and reduced density models [pdf] (June 2013).
Talk at the SIAM Conference on "Mathematical Aspects of Materials Science", Philadelphia, USA.

Efficient algorithm for two-center Coulomb and exchange integrals of electronic prolate spheroidal orbitals [pdf] (February 2012).
Talk given at CERMICS, Ecole des Ponts ParisTech, Paris, France.

Electronic structure of 3d transition metal atoms [pptx] (June 2011).
Talk at the Oberwolfach Workshop "Mathematical Methods in Quantum Chemistry", Germany.

Unital quantum channels [pdf] (December 2007).
Talk about unital quantum channels at the MPQ theory division Ringberg 2007 meeting, Germany.

Generalized functions [pdf] (March 2006).
Justification of some special fundamental solutions to well known partial differential equations in the sense of generalized functions.