Publications
Publication list on arXiv, Google Scholar
Preprints
 Qunsheng “Keefe” Huang, Christian B. Mendl
Efficient quantum circuit simulation using a multiqubit Bloch vector representation of density matrices
(arXiv:2103.13962)  Martin Knudsen, Christian B. Mendl
Solving differential equations via continuousvariable quantum computers
(arXiv:2012.12220)  Christian B. Mendl, Herbert Spohn
Highlow pressure domain wall for the classical Toda lattice
(arXiv:2011.11008)  Irene López Gutiérrez, Christian B. Mendl
Real time evolution with neuralnetwork quantum states
(arXiv:1912.08831)  Christian B. Mendl
Time evolution of matrix product operators with energy conservation
(arXiv:1812.11876)
Peer reviewed papers
2021
 Benjamin Zanger,
Christian B. Mendl,
Martin Schulz,
Martin Schreiber
Quantum algorithms for solving ordinary differential equations via classical integration methods
Quantum 5, 502 (2021) (arXiv:2012.09469)  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)  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
 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  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, 238262 (2020) (arXiv:1901.00024)
2019
 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)  Giuseppe Carleo et al.
NetKet: A machine learning toolkit for manybody quantum systems [pdf]
SoftwareX 10, 100311 (2019) (arXiv:1904.00031)  Christian B. Mendl
Fourier’s law and manybody quantum systems [pdf]
C. R. Physique 20, 442448 (2019)
2018
 ZiXiang 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)  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.  Christian B. Mendl,
Andrew Lucas
DyakonovShur instability across the ballistictohydrodynamic crossover [pdf]
Appl. Phys. Lett. 112, 124101 (2018) (arXiv:1801.01501)  Edwin W. Huang,
Christian B. Mendl,
HongChen 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)  Chunjing J. Jia, Yao Wang, Christian B. Mendl,
Brian Moritz,
Thomas P. Devereaux
Paradeisos: a perfect hashing algorithm for manybody eigenvalue problems [pdf]
Comput. Phys. Commun. 224, 8189 (2018) (arXiv:1707.03974)
2017

Edwin W. Huang, Christian B. Mendl,
Shenxiu Liu,
Steven Johnston,
HongChen Jiang,
Brian Moritz,
Thomas P. Devereaux
Numerical evidence of fluctuating stripes in the normal state of highTc cuprate superconductors [pdf]
Science 358, 11611164 (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.  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 HubbardHolstein model [pdf]
Phys. Rev. B 96, 205141 (2017) (arXiv:1709.00245)  Annabelle Bohrdt, Christian B. Mendl,
Manuel Endres,
Michael Knap
Scrambling and thermalization in a diffusive quantum manybody 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.  Christian B. Mendl, Herbert Spohn
Shocks, rarefaction waves, and current fluctuations for anharmonic chains [pdf]
J. Stat. Phys. 166, 841875 (2017) (arXiv:1607.05205)
Detailed derivations related to the publication “Searching for the TracyWidom distribution in nonequilibrium processes” below.
2016
 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”.  Christian B. Mendl, Herbert Spohn
Searching for the TracyWidom distribution in nonequilibrium processes [pdf]
Phys. Rev. E 93, 060101(R) (2016) (arXiv:1512.06292)
The height fluctuations for onedimensional growth models in the KardarParisiZhang universality class are governed by the random matrix TracyWidom distribution. Here we demonstrate that the TracyWidom distribution also occurs for the Leroux stochastic lattice gas and hardpoint 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 onedimensional quantum fluids.  Christian B. Mendl
Efficient algorithm for manyelectron angular momentum and spin diagonalization on atomic subshells [pdf]
Commun. Comput. Phys. 19, 192204 (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 asymptoticsbased configurationinteraction methods and electronic structure of transition metal atoms” below.
2015
 Christian B. Mendl, Herbert Spohn
Low temperature dynamics of the onedimensional 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.  Francesc Malet,
André Mirtschink, Christian B. Mendl, Johannes Bjerlin, Elife Ö. Karabulut,
Stephanie M. Reimann,
Paola GoriGiorgi
Density functional theory for stronglycorrelated 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 longranged interactions. Also refer to the paper “Wigner localization in quantum dots from KohnSham density functional theory without symmetry breaking” below.  Jianfeng Lu, Christian B. Mendl
Numerical scheme for a spatially inhomogeneous matrixvalued quantum Boltzmann equation [pdf]
J. Comput. Phys. 291, 303316 (2015) (arXiv:1408.1782)
Development and implementation of an efficient algorithm for the spatially inhomogeneous matrixvalued quantum Boltzmann equation derived from the Hubbard model. Also compare with the BoltzmannHubbard papers below concerned with the onedimensional case.  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 timecorrelation functions for onedimensional hardpoint systems” and “Dynamic correlators of FermiPastaUlam chains and nonlinear fluctuating hydrodynamics” below.  Christian B. Mendl
Matrixvalued quantum lattice Boltzmann method [pdf]
Int. J. Mod. Phys. C 26, 1550113 (2015) (arXiv:1309.1656)
Lattice Boltzmann method (LBM) with quantum aspects: FermiDirac equilibrium functions instead of MaxwellBoltzmann, and matrixvalued spin density matrices as distribution functions. See also the video in the software section.  Martin L.R. Fürst, Markus Kotulla, Christian B. Mendl, Herbert Spohn
Quantum Boltzmann equation for spindependent reactions in the kinetic regime [pdf]
J. Phys. A 48, 095204 (2015) (arXiv:1411.2576)
Matrixvalued multicomponent Boltzmann equation derived from a general quantum field Hamiltonian. We illustrate the approach to equilibrium by numerical simulations in the isotropic threedimensional setting.
2014
 Huajie Chen, Gero Friesecke, Christian B. Mendl
Numerical methods for a KohnSham density functional model based on optimal transport [pdf]
J. Chem. Theory Comput. 10, 43604368 (2014) (arXiv:1405.7026)
Finite element discretization of the optimal transport map for N = 2 electrons.  Christian B. Mendl, Herbert Spohn
Equilibrium timecorrelation functions for onedimensional hardpoint systems [pdf]
Phys. Rev. E 90, 012147 (2014) (arXiv:1403.0213)
Comparing molecular dynamics simulations of hardpoint 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 FermiPastaUlam chains and nonlinear fluctuating hydrodynamics” below and the paper by Herbert Spohn “Nonlinear fluctuating hydrodynamics for anharmonic chains”, J. Stat. Phys. 154, 11911227 (2014).  Suman G. Das, Abhishek Dhar,
Keiji Saito,
Christian B. Mendl, Herbert Spohn
Numerical test of hydrodynamic fluctuation theory in the FermiPastaUlam chain [pdf]
Phys. Rev. E 90, 012124 (2014) (arXiv:1404.7081)  Martin L.R. Fürst, Christian B. Mendl, Herbert Spohn
Dynamics of the BoseHubbard chain for weak interactions [pdf]
Phys. Rev. B 89, 134311 (2014) (arXiv:1312.6737)
Matrixvalued Boltzmann equation for the BoseHubbard chain in the kinetic regime, including a theoretical derivation and numerical simulations. Concerning the FermiHubbard chain, see the papers below.  Christian B. Mendl, Francesc Malet, Paola GoriGiorgi
Wigner localization in quantum dots from KohnSham density functional theory without symmetry breaking [pdf]
Phys. Rev. B 89, 125106 (2014) (arXiv:1311.6011)
KohnSham 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
 Christian B. Mendl, Herbert Spohn
Dynamic correlators of FermiPastaUlam 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.  Gero Friesecke, Christian B. Mendl,
Brendan Pass, Codina Cotar,
Claudia Klüppelberg
Ndensity representability and the optimal transport limit of the HohenbergKohn 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.  Martin L.R. Fürst, Christian B. Mendl, Herbert Spohn
Matrixvalued Boltzmann equation for the nonintegrable Hubbard chain [pdf]
Phys. Rev. E 88, 012108 (2013) (arXiv:1302.2075)
Followup paper for the nonintegrable 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.  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.  Christian B. Mendl, Steven Eliuk, Michelle Noga, and Pierre Boulanger
Comprehensive analysis of highperformance computing methods for filtered backprojection [pdf]
ELCVIA 12(1): 116 (2013)
Based on the Radon transform implementation in the software section, but for fanbeam geometry.
2012
 Martin L.R. Fürst, Christian B. Mendl, Herbert Spohn
Matrixvalued Boltzmann equation for the Hubbard chain [pdf]
Phys. Rev. E 86, 031122 (2012) (arXiv:1207.6926)
The timedependent Wigner function is matrixvalued due to spin.  Christian B. Mendl
Efficient algorithm for twocenter Coulomb and exchange integrals of electronic prolate spheroidal orbitals [pdf]
J. Comput. Phys. 231, 51575175 (2012) (arXiv:1203.6256)
The paper presents a fast algorithm to calculate Coulomb/exchange integrals of prolate spheroidal electronic orbitals, which appear in diatomic molecules. The Mathematica code used for the calculations in the paper is available at GitHub.
2011
 Christian B. Mendl
The FermiFab toolbox for fermionic manyparticle quantum systems [pdf]
Comput. Phys. Commun. 182, 13271337 (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
 Christian B. Mendl, Gero Friesecke
Efficient algorithm for asymptoticsbased configurationinteraction 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

Christian B. Mendl, Michael M. Wolf
Unital quantum channels  Convex structure and revivals of Birkhoff’s theorem [pdf]
Commun. Math. Phys. 289, 10571086 (2009) (arXiv:0806.2820)
Basically a compact version of my physics diploma thesis.
Book chapters and conference reports
 Christian B. Mendl, Silvia Palpacelli,
Alex Kamenev,
Sauro Succi
Quantum lattice Boltzmann study of randommass Dirac fermions in one dimension [pdf]
In: G. Angilella, C. Amovilli (eds) Manybody Approaches at Different Scales. Springer, Cham [doi], (arXiv:1706.05138)  Christian B. Mendl
Electronic structure of 3d transition metal atoms [pdf]
Oberwolfach Reports 8 (2011), issue 2, pp. 17691843
Mathematical Methods in Quantum Chemistry
Selected Talks and Notes
 Real time evolution with neuralnetwork quantum states by approximating the implicit midpoint method
[pdf] (June 2020).
Virtual talk at the Machine Learning for Quantum Simulation: Virtual Conference, Flatiron Institute, USA.  Kinetic Theory of the DyakonovShur Instability
[pdf] (March 2018).
Talk at the APS March meeting 2018, Los Angeles, USA.  Matrixvalued Quantum Boltzmann Methods
[pdf] (November 2016).
Talk at the KINet Young Researchers Workshop: Stochastic and deterministic methods in kinetic theory, Duke University, USA.  Searching for the TracyWidom 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 HubbardHolstein model
[pdf] (March 2016).
Talk at the APS March meeting 2016, Baltimore, USA.  Low temperature dynamics of the onedimensional discrete nonlinear Schrödinger equation
[pdf] (February 2016).
Talk at the workshop “New approaches to nonequilibrium and random systems”, KITP, UC Santa Barbara, USA.  KohnSham 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”, KonradZuse Institut Berlin, Germany.  Optimal transport limit of the HohenbergKohn 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 twocenter 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.
PhD Statistical (Bio)Physics
I’ve completed my PhD at the LudwigMaximiliansUniversität München, supervised by Prof. Dr. Tim Gollisch and Prof. Dr. Erwin Frey. Experimental work was performed at the MaxPlanckInstitute 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
Diploma Thesis:  Unital quantum channels [pdf] (June 2008, 60 pages) 
Advisors:  Prof. Dr. J. Ignacio Cirac, Prof. Dr. Michael M. Wolf 
Address:  Theory Division MaxPlanckInstitut für Quantenoptik HansKopfermannStraße 1 D85748 Garching bei München 
Mathematics
Diploma Thesis:  The Nrepresentability problem and orbital occupation in transition metals [pdf] (July 2008, 58 pages) 
Bachelor Thesis:  The representability problem in manybody quantum mechanics [pdf] (October 2006, 32 pages) 
Advisor:  Prof. PhD. Gero Friesecke 
Address:  Department of Mathematics  Global Analysis Technische Universität München Boltzmannstraße 3 D85747 Garching bei München 