Publications

Publication list on arXiv, Google Scholar

Preprints

  1. Qunsheng “Keefe” Huang, Christian B. Mendl
    Efficient quantum circuit simulation using a multi-qubit Bloch vector representation of density matrices
    (arXiv:2103.13962)
  2. Martin Knudsen, Christian B. Mendl
    Solving differential equations via continuous-variable quantum computers
    (arXiv:2012.12220)
  3. Benjamin Zanger, Christian B. Mendl, Martin Schulz, Martin Schreiber
    Quantum algorithms for solving ordinary differential equations
    (arXiv:2012.09469)
  4. Christian B. Mendl, Herbert Spohn
    High-low pressure domain wall for the classical Toda lattice
    (arXiv:2011.11008)
  5. Irene López Gutiérrez, Christian B. Mendl
    Real time evolution with neural-network quantum states
    (arXiv:1912.08831)
  6. Christian B. Mendl
    Time evolution of matrix product operators with energy conservation
    (arXiv:1812.11876)

Peer reviewed papers

2021

  1. Christian B. Mendl, Folkmar Bornemann
    Efficient numerical evaluation of thermodynamic quantities on infinite (semi-)classical chains
    J. Stat. Phys. 182, 57 (2021) (arXiv:2006.13587)
  2. Christian B. Mendl, Marco Polini, Andrew Lucas
    Coherent terahertz radiation from a nonlinear oscillator of viscous electrons [pdf]
    Appl. Phys. Lett. 118, 013105 (2021) (arXiv:1909.11093)

2020

  1. Lisa Sahlmann, Christian B. Mendl
    GuiTeNet: A graphical user interface for tensor networks
    J. Open Res. Softw. 8(1), 29 (2020) (arXiv:1808.00532)
    Online demo at guitenet.org
  2. Avijit Das, Kedar Damle, Abhishek Dhar, David A. Huse, Manas Kulkarni, Christian B. Mendl, Herbert Spohn
    Nonlinear fluctuating hydrodynamics for the classical XXZ spin chain [pdf]
    J. Stat. Phys. 180, 238-262 (2020) (arXiv:1901.00024)

2019

  1. Christian B. Mendl, Jan Carl Budich
    Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems [pdf]
    Phys. Rev. B 100, 224307 (2019) (arXiv:1909.01402)
  2. Giuseppe Carleo et al.
    NetKet: A machine learning toolkit for many-body quantum systems [pdf]
    SoftwareX 10, 100311 (2019) (arXiv:1904.00031)
  3. Christian B. Mendl
    Fourier’s law and many-body quantum systems [pdf]
    C. R. Physique 20, 442-448 (2019)

2018

  1. Zi-Xiang Li, Abolhassan Vaezi, Christian B. Mendl, Hong Yao
    Numerical observation of emergent spacetime supersymmetry at quantum criticality [pdf]
    Sci. Adv. 4, eaau1463 (2018) (arXiv:1711.04772)
  2. Christian B. Mendl
    PyTeNet: A concise Python implementation of quantum tensor network algorithms [pdf]
    Journal of Open Source Software 3(30), 948 (2018)
    PyTeNet is hosted at GitHub.
  3. Christian B. Mendl, Andrew Lucas
    Dyakonov-Shur instability across the ballistic-to-hydrodynamic crossover [pdf]
    Appl. Phys. Lett. 112, 124101 (2018) (arXiv:1801.01501)
  4. Edwin W. Huang, Christian B. Mendl, Hong-Chen Jiang, Brian Moritz, Thomas P. Devereaux
    Stripe order from the perspective of the Hubbard model [pdf]
    npj Quantum Mater. 3, 22 (2018) (arXiv:1709.02398)
  5. Chunjing J. Jia, Yao Wang, Christian B. Mendl, Brian Moritz, Thomas P. Devereaux
    Paradeisos: a perfect hashing algorithm for many-body eigenvalue problems [pdf]
    Comput. Phys. Commun. 224, 81-89 (2018) (arXiv:1707.03974)

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) (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) (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) (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) (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) (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) (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) (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 (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) (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) (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 (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) (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) (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) (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) (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) (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) (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) (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) (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) (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) (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) (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)
    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) (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) (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) (arXiv:1103.0872)
    This paper descibes the FermiFab Matlab and Mathematica toolbox (available at GitHub, formerly 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) (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) (arXiv:0806.2820)
    Basically a compact version of my physics diploma thesis.

Book chapters and conference reports

  1. Christian B. Mendl, Silvia Palpacelli, Alex Kamenev, Sauro Succi
    Quantum lattice Boltzmann study of random-mass Dirac fermions in one dimension [pdf]
    In: G. Angilella, C. Amovilli (eds) Many-body Approaches at Different Scales. Springer, Cham [doi], (arXiv:1706.05138)
  2. Christian B. Mendl
    Electronic structure of 3d transition metal atoms [pdf]
    Oberwolfach Reports 8 (2011), issue 2, pp. 1769-1843
    Mathematical Methods in Quantum Chemistry

Selected Talks and Notes

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

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