TY - JOUR
AB - This paper deals with dynamical optimal transport metrics defined by spatial discretisation of the Benamou–Benamou formula for the Kantorovich metric . Such metrics appear naturally in discretisations of -gradient flow formulations for dissipative PDE. However, it has recently been shown that these metrics do not in general converge to , unless strong geometric constraints are imposed on the discrete mesh. In this paper we prove that, in a 1-dimensional periodic setting, discrete transport metrics converge to a limiting transport metric with a non-trivial effective mobility. This mobility depends sensitively on the geometry of the mesh and on the non-local mobility at the discrete level. Our result quantifies to what extent discrete transport can make use of microstructure in the mesh to reduce the cost of transport.
AU - Gladbach, Peter
AU - Kopfer, Eva
AU - Maas, Jan
AU - Portinale, Lorenzo
ID - 7573
JF - Journal des Mathematiques Pures et Appliquees
SN - 00217824
TI - Homogenisation of one-dimensional discrete optimal transport
ER -
TY - JOUR
AB - The eukaryotic endomembrane system is controlled by small GTPases of the Rab family, which are activated at defined times and locations in a switch-like manner. While this switch is well understood for an individual protein, how regulatory networks produce intracellular activity patterns is currently not known. Here, we combine in vitro reconstitution experiments with computational modeling to study a minimal Rab5 activation network. We find that the molecular interactions in this system give rise to a positive feedback and bistable collective switching of Rab5. Furthermore, we find that switching near the critical point is intrinsically stochastic and provide evidence that controlling the inactive population of Rab5 on the membrane can shape the network response. Notably, we demonstrate that collective switching can spread on the membrane surface as a traveling wave of Rab5 activation. Together, our findings reveal how biochemical signaling networks control vesicle trafficking pathways and how their nonequilibrium properties define the spatiotemporal organization of the cell.
AU - Bezeljak, Urban
AU - Loya, Hrushikesh
AU - Kaczmarek, Beata M
AU - Saunders, Timothy E.
AU - Loose, Martin
ID - 7580
IS - 12
JF - Proceedings of the National Academy of Sciences
SN - 0027-8424
TI - Stochastic activation and bistability in a Rab GTPase regulatory network
VL - 117
ER -
TY - JOUR
AB - Small RNAs (smRNA, 19–25 nucleotides long), which are transcribed by RNA polymerase II, regulate the expression of genes involved in a multitude of processes in eukaryotes. miRNA biogenesis and the proteins involved in the biogenesis pathway differ across plant and animal lineages. The major proteins constituting the biogenesis pathway, namely, the Dicers (DCL/DCR) and Argonautes (AGOs), have been extensively studied. However, the accessory proteins (DAWDLE (DDL), SERRATE (SE), and TOUGH (TGH)) of the pathway that differs across the two lineages remain largely uncharacterized. We present the first detailed report on the molecular evolution and divergence of these proteins across eukaryotes. Although DDL is present in eukaryotes and prokaryotes, SE and TGH appear to be specific to eukaryotes. The addition/deletion of specific domains and/or domain-specific sequence divergence in the three proteins points to the observed functional divergence of these proteins across the two lineages, which correlates with the differences in miRNA length across the two lineages. Our data enhance the current understanding of the structure–function relationship of these proteins and reveals previous unexplored crucial residues in the three proteins that can be used as a basis for further functional characterization. The data presented here on the number of miRNAs in crown eukaryotic lineages are consistent with the notion of the expansion of the number of miRNA-coding genes in animal and plant lineages correlating with organismal complexity. Whether this difference in functionally correlates with the diversification (or presence/absence) of the three proteins studied here or the miRNA signaling in the plant and animal lineages is unclear. Based on our results of the three proteins studied here and previously available data concerning the evolution of miRNA genes in the plant and animal lineages, we believe that miRNAs probably evolved once in the ancestor to crown eukaryotes and have diversified independently in the eukaryotes.
AU - Moturu, Taraka Ramji
AU - Sinha, Sansrity
AU - Salava, Hymavathi
AU - Thula, Sravankumar
AU - Nodzyński, Tomasz
AU - Vařeková, Radka Svobodová
AU - Friml, Jiří
AU - Simon, Sibu
ID - 7582
IS - 3
JF - Plants
TI - Molecular evolution and diversification of proteins involved in miRNA maturation pathway
VL - 9
ER -
TY - JOUR
AB - CLC chloride/proton exchangers may support acidification of endolysosomes and raise their luminal Cl− concentration. Disruption of endosomal ClC‐3 causes severe neurodegeneration. To assess the importance of ClC‐3 Cl−/H+ exchange, we now generate Clcn3unc/unc mice in which ClC‐3 is converted into a Cl− channel. Unlike Clcn3−/− mice, Clcn3unc/unc mice appear normal owing to compensation by ClC‐4 with which ClC‐3 forms heteromers. ClC‐4 protein levels are strongly reduced in Clcn3−/−, but not in Clcn3unc/unc mice because ClC‐3unc binds and stabilizes ClC‐4 like wild‐type ClC‐3. Although mice lacking ClC‐4 appear healthy, its absence in Clcn3unc/unc/Clcn4−/− mice entails even stronger neurodegeneration than observed in Clcn3−/− mice. A fraction of ClC‐3 is found on synaptic vesicles, but miniature postsynaptic currents and synaptic vesicle acidification are not affected in Clcn3unc/unc or Clcn3−/− mice before neurodegeneration sets in. Both, Cl−/H+‐exchange activity and the stabilizing effect on ClC‐4, are central to the biological function of ClC‐3.
AU - Weinert, Stefanie
AU - Gimber, Niclas
AU - Deuschel, Dorothea
AU - Stuhlmann, Till
AU - Puchkov, Dmytro
AU - Farsi, Zohreh
AU - Ludwig, Carmen F.
AU - Novarino, Gaia
AU - López-Cayuqueo, Karen I.
AU - Planells-Cases, Rosa
AU - Jentsch, Thomas J.
ID - 7586
JF - EMBO Journal
SN - 02614189
TI - Uncoupling endosomal CLC chloride/proton exchange causes severe neurodegeneration
ER -
TY - JOUR
AB - The concept of the entanglement between spin and orbital degrees of freedom plays a crucial role in our understanding of various phases and exotic ground states in a broad class of materials, including orbitally ordered materials and spin liquids. We investigate how the spin-orbital entanglement in a Mott insulator depends on the value of the spin-orbit coupling of the relativistic origin. To this end, we numerically diagonalize a one-dimensional spin-orbital model with Kugel-Khomskii exchange interactions between spins and orbitals on different sites supplemented by the on-site spin-orbit coupling. In the regime of small spin-orbit coupling with regard to the spin-orbital exchange, the ground state to a large extent resembles the one obtained in the limit of vanishing spin-orbit coupling. On the other hand, for large spin-orbit coupling the ground state can, depending on the model parameters, either still show negligible spin-orbital entanglement or evolve to a highly spin-orbitally-entangled phase with completely distinct properties that are described by an effective XXZ model. The presented results suggest that (i) the spin-orbital entanglement may be induced by large on-site spin-orbit coupling, as found in the 5d transition metal oxides, such as the iridates; (ii) for Mott insulators with weak spin-orbit coupling of Ising type, such as, e.g., the alkali hyperoxides, the effects of the spin-orbit coupling on the ground state can, in the first order of perturbation theory, be neglected.
AU - Gotfryd, Dorota
AU - Paerschke, Ekaterina
AU - Chaloupka, Jiri
AU - Oles, Andrzej M.
AU - Wohlfeld, Krzysztof
ID - 7594
IS - 1
JF - Physical Review Research
TI - How spin-orbital entanglement depends on the spin-orbit coupling in a Mott insulator
VL - 2
ER -
TY - JOUR
AB - Directional intercellular transport of the phytohormone auxin mediated by PIN FORMED (PIN) efflux carriers plays essential roles in both coordinating patterning processes and integrating multiple external cues by rapidly redirecting auxin fluxes. Multilevel regulations of PIN activity under internal and external cues are complicated; however, the underlying molecular mechanism remains elusive. Here we demonstrate that 3’-Phosphoinositide-Dependent Protein Kinase1 (PDK1), which is conserved in plants and mammals, functions as a molecular hub integrating the upstream lipid signalling and the downstream substrate activity through phosphorylation. Genetic analysis uncovers that loss-of-function Arabidopsis mutant pdk1.1 pdk1.2 exhibits a plethora of abnormalities in organogenesis and growth, due to the defective PIN-dependent auxin transport. Further cellular and biochemical analyses reveal that PDK1 phosphorylates D6 Protein Kinase to facilitate its activity towards PIN proteins. Our studies establish a lipid-dependent phosphorylation cascade connecting membrane composition-based cellular signalling with plant growth and patterning by regulating morphogenetic auxin fluxes.
AU - Tan, Shutang
AU - Zhang, Xixi
AU - Kong, Wei
AU - Yang, Xiao-Li
AU - Molnar, Gergely
AU - Vondráková, Zuzana
AU - Filepová, Roberta
AU - Petrášek, Jan
AU - Friml, Jiří
AU - Xue, Hong-Wei
ID - 7600
JF - Nature Plants
TI - The lipid code-dependent phosphoswitch PDK1–D6PK activates PIN-mediated auxin efflux in Arabidopsis
VL - 6
ER -
TY - GEN
AB - Plasmodesmata (PD) are crucial structures for intercellular communication in multicellular plants with remorins being their crucial plant-specific structural and functional constituents. The PD biogenesis is an intriguing but poorly understood process. By expressing an Arabidopsis remorin protein in mammalian cells, we have reconstituted a PD-like filamentous structure, termed remorin filament (RF), connecting neighboring cells physically and physiologically. Notably, RFs are capable of transporting macromolecules intercellularly, in a way similar to plant PD. With further super-resolution microscopic analysis and biochemical characterization, we found that RFs are also composed of actin filaments, forming the core skeleton structure, aligned with the remorin protein. This unique heterologous filamentous structure might explain the molecular mechanism for remorin function as well as PD construction. Furthermore, remorin protein exhibits a specific distribution manner in the plasma membrane in mammalian cells, representing a lipid nanodomain, depending on its lipid modification status. Our studies not only provide crucial insights into the mechanism of PD biogenesis, but also uncovers unsuspected fundamental mechanistic and evolutionary links between intercellular communication systems of plants and animals.
AU - Wei, Zhuang
AU - Tan, Shutang
AU - Liu, Tao
AU - Wu, Yuan
AU - Lei, Ji-Gang
AU - Chen, ZhengJun
AU - Friml, Jiří
AU - Xue, Hong-Wei
AU - Liao, Kan
ID - 7601
T2 - bioRxiv
TI - Plasmodesmata-like intercellular connections by plant remorin in animal cells
ER -
TY - CONF
AB - Union-Find (or Disjoint-Set Union) is one of the fundamental problems in computer science; it has been well-studied from both theoretical and practical perspectives in the sequential case. Recently, there has been mounting interest in analyzing this problem in the concurrent scenario, and several asymptotically-efficient algorithms have been proposed. Yet, to date, there is very little known about the practical performance of concurrent Union-Find. This work addresses this gap. We evaluate and analyze the performance of several concurrent Union-Find algorithms and optimization strategies across a wide range of platforms (Intel, AMD, and ARM) and workloads (social, random, and road networks, as well as integrations into more complex algorithms). We first observe that, due to the limited computational cost, the number of induced cache misses is the critical determining factor for the performance of existing algorithms. We introduce new techniques to reduce this cost by storing node priorities implicitly and by using plain reads and writes in a way that does not affect the correctness of the algorithms. Finally, we show that Union-Find implementations are an interesting application for Transactional Memory (TM): one of the fastest algorithm variants we discovered is a sequential one that uses coarse-grained locking with the lock elision optimization to reduce synchronization cost and increase scalability.
AU - Alistarh, Dan-Adrian
AU - Fedorov, Alexander
AU - Koval, Nikita
ID - 7605
SN - 18688969
TI - In search of the fastest concurrent union-find algorithm
VL - 153
ER -
TY - JOUR
AB - We consider a system of N bosons in the limit N→∞, interacting through singular potentials. For initial data exhibiting Bose–Einstein condensation, the many-body time evolution is well approximated through a quadratic fluctuation dynamics around a cubic nonlinear Schrödinger equation of the condensate wave function. We show that these fluctuations satisfy a (multi-variate) central limit theorem.
AU - Rademacher, Simone Anna Elvira
ID - 7611
JF - Letters in Mathematical Physics
SN - 0377-9017
TI - Central limit theorem for Bose gases interacting through singular potentials
ER -
TY - JOUR
AB - This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger divergences that are of the form ϕ(A,B)=Tr((1−c)A+cB−AσB), where σ is an arbitrary Kubo–Ando mean, and c∈(0,1) is the weight of σ. We note that these divergences belong to the family of maximal quantum f-divergences, and hence are jointly convex, and satisfy the data processing inequality. We derive a characterization of the barycenter of finitely many positive definite operators for these generalized quantum Hellinger divergences. We note that the characterization of the barycenter as the weighted multivariate 1/2-power mean, that was claimed in Bhatia et al. (2019), is true in the case of commuting operators, but it is not correct in the general case.
AU - Pitrik, Jozsef
AU - Virosztek, Daniel
ID - 7618
IS - 8
JF - Letters in Mathematical Physics
SN - 0377-9017
TI - Quantum Hellinger distances revisited
VL - 110
ER -
TY - JOUR
AB - Cell polarity is a fundamental feature of all multicellular organisms. In plants, prominent cell polarity markers are PIN auxin transporters crucial for plant development. To identify novel components involved in cell polarity establishment and maintenance, we carried out a forward genetic screening with PIN2:PIN1-HA;pin2 Arabidopsis plants, which ectopically express predominantly basally localized PIN1 in the root epidermal cells leading to agravitropic root growth. From the screen, we identified the regulator of PIN polarity 12 (repp12) mutation, which restored gravitropic root growth and caused PIN1-HA polarity switch from basal to apical side of root epidermal cells. Complementation experiments established the repp12 causative mutation as an amino acid substitution in Aminophospholipid ATPase3 (ALA3), a phospholipid flippase with predicted function in vesicle formation. ala3 T-DNA mutants show defects in many auxin-regulated processes, in asymmetric auxin distribution and in PIN trafficking. Analysis of quintuple and sextuple mutants confirmed a crucial role of ALA proteins in regulating plant development and in PIN trafficking and polarity. Genetic and physical interaction studies revealed that ALA3 functions together with GNOM and BIG3 ARF GEFs. Taken together, our results identified ALA3 flippase as an important interactor and regulator of ARF GEF functioning in PIN polarity, trafficking and auxin-mediated development.
AU - Zhang, Xixi
AU - Adamowski, Maciek
AU - Marhavá, Petra
AU - Tan, Shutang
AU - Zhang, Yuzhou
AU - Rodriguez Solovey, Lesia
AU - Zwiewka, Marta
AU - Pukyšová, Vendula
AU - Sánchez, Adrià Sans
AU - Raxwal, Vivek Kumar
AU - Hardtke, Christian S.
AU - Nodzynski, Tomasz
AU - Friml, Jiří
ID - 7619
IS - 5
JF - The Plant Cell
SN - 1040-4651
TI - Arabidopsis flippases cooperate with ARF GTPase exchange factors to regulate the trafficking and polarity of PIN auxin transporters
VL - 32
ER -
TY - JOUR
AB - A two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modeled as an elastic curve, subject to an internal pressure force. Net polymerization or depolymerization in the cortex is modeled via local addition or removal of material, driving a cortical flow. The model takes the form of a fully nonlinear degenerate parabolic system. An existence analysis is carried out by adapting ideas from the theory of gradient flows. Numerical simulations show that these simple rules can account for the behavior observed in experiments, suggesting a possible mechanical mechanism for adhesion-independent motility.
AU - Jankowiak, Gaspard
AU - Peurichard, Diane
AU - Reversat, Anne
AU - Schmeiser, Christian
AU - Sixt, Michael K
ID - 7623
JF - Mathematical Models and Methods in Applied Sciences
SN - 02182025
TI - Modeling adhesion-independent cell migration
ER -
TY - THES
AB - This thesis is based on three main topics: In the first part, we study convergence of discrete gradient flow structures associated with regular finite-volume discretisations of Fokker-Planck equations. We show evolutionary I convergence of the discrete gradient flows to the L2-Wasserstein gradient flow corresponding to the solution of a Fokker-Planck
equation in arbitrary dimension d >= 1. Along the argument, we prove Mosco- and I-convergence results for discrete energy functionals, which are of independent interest for convergence of equivalent gradient flow structures in Hilbert spaces.
The second part investigates L2-Wasserstein flows on metric graph. The starting point is a Benamou-Brenier formula for the L2-Wasserstein distance, which is proved via a regularisation scheme for solutions of the continuity equation, adapted to the peculiar geometric structure of metric graphs. Based on those results, we show that the L2-Wasserstein space over a metric graph admits a gradient flow which may be identified as a solution of a Fokker-Planck equation.
In the third part, we focus again on the discrete gradient flows, already encountered in the first part. We propose a variational structure which extends the gradient flow structure to Markov chains violating the detailed-balance conditions. Using this structure, we characterise contraction estimates for the discrete heat flow in terms of convexity of
corresponding path-dependent energy functionals. In addition, we use this approach to derive several functional inequalities for said functionals.
AU - Forkert, Dominik L
ID - 7629
SN - 2663-337X
TI - Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains
ER -
TY - JOUR
AB - The posterior parietal cortex (PPC) and frontal motor areas comprise a cortical network supporting goal-directed behaviour, with functions including sensorimotor transformations and decision making. In primates, this network links performed and observed actions via mirror neurons, which fire both when individuals perform an action and when they observe the same action performed by a conspecific. Mirror neurons are believed to be important for social learning, but it is not known whether mirror-like neurons occur in similar networks in other social species, such as rodents, or if they can be measured in such models using paradigms where observers passively view a demonstrator. Therefore, we imaged Ca2+ responses in PPC and secondary motor cortex (M2) while mice performed and observed pellet-reaching and wheel-running tasks, and found that cell populations in both areas robustly encoded several naturalistic behaviours. However, neural responses to the same set of observed actions were absent, although we verified that observer mice were attentive to performers and that PPC neurons responded reliably to visual cues. Statistical modelling also indicated that executed actions outperformed observed actions in predicting neural responses. These results raise the possibility that sensorimotor action recognition in rodents could take place outside of the parieto-frontal circuit, and underscore that detecting socially-driven neural coding depends critically on the species and behavioural paradigm used.
AU - Tombaz, Tuce
AU - Dunn, Benjamin A.
AU - Hovde, Karoline
AU - Cubero, Ryan J
AU - Mimica, Bartul
AU - Mamidanna, Pranav
AU - Roudi, Yasser
AU - Whitlock, Jonathan R.
ID - 7632
IS - 1
JF - Scientific reports
TI - Action representation in the mouse parieto-frontal network
VL - 10
ER -
TY - JOUR
AB - Assemblies of colloidal semiconductor nanocrystals (NCs) in the form of thin solid films leverage the size-dependent quantum confinement properties and the wet chemical methods vital for the development of the emerging solution-processable electronics, photonics, and optoelectronics technologies. The ability to control the charge carrier transport in the colloidal NC assemblies is fundamental for altering their electronic and optical properties for the desired applications. Here we demonstrate a strategy to render the solids of narrow-bandgap NC assemblies exclusively electron-transporting by creating a type-II heterojunction via shelling. Electronic transport of molecularly cross-linked PbTe@PbS core@shell NC assemblies is measured using both a conventional solid gate transistor and an electric-double-layer transistor, as well as compared with those of core-only PbTe NCs. In contrast to the ambipolar characteristics demonstrated by many narrow-bandgap NCs, the core@shell NCs exhibit exclusive n-type transport, i.e., drastically suppressed contribution of holes to the overall transport. The PbS shell that forms a type-II heterojunction assists the selective carrier transport by heavy doping of electrons into the PbTe-core conduction level and simultaneously strongly localizes the holes within the NC core valence level. This strongly enhanced n-type transport makes these core@shell NCs suitable for applications where ambipolar characteristics should be actively suppressed, in particular, for thermoelectric and electron-transporting layers in photovoltaic devices.
AU - Miranti, Retno
AU - Shin, Daiki
AU - Septianto, Ricky Dwi
AU - Ibáñez, Maria
AU - Kovalenko, Maksym V.
AU - Matsushita, Nobuhiro
AU - Iwasa, Yoshihiro
AU - Bisri, Satria Zulkarnaen
ID - 7634
IS - 3
JF - ACS Nano
TI - Exclusive electron transport in Core@Shell PbTe@PbS colloidal semiconductor nanocrystal assemblies
VL - 14
ER -
TY - CONF
AB - Concurrent programming can be notoriously complex and error-prone. Programming bugs can arise from a variety of sources, such as operation re-reordering, or incomplete understanding of the memory model. A variety of formal and model checking methods have been developed to address this fundamental difficulty. While technically interesting, existing academic methods are still hard to apply to the large codebases typical of industrial deployments, which limits their practical impact.
AU - Koval, Nikita
AU - Sokolova, Mariia
AU - Fedorov, Alexander
AU - Alistarh, Dan-Adrian
AU - Tsitelov, Dmitry
ID - 7635
SN - 9781450368186
T2 - Proceedings of the ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPOPP
TI - Testing concurrency on the JVM with Lincheck
ER -
TY - CONF
AB - Balanced search trees typically use key comparisons to guide their operations, and achieve logarithmic running time. By relying on numerical properties of the keys, interpolation search achieves lower search complexity and better performance. Although interpolation-based data structures were investigated in the past, their non-blocking concurrent variants have received very little attention so far.
In this paper, we propose the first non-blocking implementation of the classic interpolation search tree (IST) data structure. For arbitrary key distributions, the data structure ensures worst-case O(log n + p) amortized time for search, insertion and deletion traversals. When the input key distributions are smooth, lookups run in expected O(log log n + p) time, and insertion and deletion run in expected amortized O(log log n + p) time, where p is a bound on the number of threads. To improve the scalability of concurrent insertion and deletion, we propose a novel parallel rebuilding technique, which should be of independent interest.
We evaluate whether the theoretical improvements translate to practice by implementing the concurrent interpolation search tree, and benchmarking it on uniform and nonuniform key distributions, for dataset sizes in the millions to billions of keys. Relative to the state-of-the-art concurrent data structures, the concurrent interpolation search tree achieves performance improvements of up to 15% under high update rates, and of up to 50% under moderate update rates. Further, ISTs exhibit up to 2X less cache-misses, and consume 1.2 -- 2.6X less memory compared to the next best alternative on typical dataset sizes. We find that the results are surprisingly robust to distributional skew, which suggests that our data structure can be a promising alternative to classic concurrent search structures.
AU - Brown, Trevor A
AU - Prokopec, Aleksandar
AU - Alistarh, Dan-Adrian
ID - 7636
SN - 9781450368186
T2 - Proceedings of the ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPOPP
TI - Non-blocking interpolation search trees with doubly-logarithmic running time
ER -
TY - JOUR
AB - The evolution of finitely many particles obeying Langevin dynamics is described by Dean–Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz multiplicative noise in divergence form. We derive a regularised Dean–Kawasaki model based on second order Langevin dynamics by analysing a system of particles interacting via a pairwise potential. Key tools of our analysis are the propagation of chaos and Simon's compactness criterion. The model we obtain is a small-noise stochastic perturbation of the undamped McKean–Vlasov equation. We also provide a high-probability result for existence and uniqueness for our model.
AU - Cornalba, Federico
AU - Shardlow, Tony
AU - Zimmer, Johannes
ID - 7637
IS - 2
JF - Nonlinearity
SN - 09517715
TI - From weakly interacting particles to a regularised Dean-Kawasaki model
VL - 33
ER -
TY - JOUR
AB - Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide exact formulae of broad applicability for the time-dependence of expectation values and correlation functions following a quantum quench in terms of averages over classical stochastic processes. We further explore the behavior of the classical stochastic variables in the presence of dynamical quantum phase transitions, including results for their distributions and correlation functions. We provide details on the numerical solution of the associated stochastic differential equations, and examine the growth of fluctuations in the classical description. We discuss the strengths and limitations of the current implementation of the stochastic approach and the potential for further development.
AU - De Nicola, Stefano
AU - Doyon, B.
AU - Bhaseen, M. J.
ID - 7638
IS - 1
JF - Journal of Statistical Mechanics: Theory and Experiment
TI - Non-equilibrium quantum spin dynamics from classical stochastic processes
VL - 2020
ER -
TY - JOUR
AB - We consider a dilute, homogeneous Bose gas at positive temperature. The system is investigated in the Gross–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 4πa(2ϱ2−ϱ20). Here ϱ denotes the density of the system and ϱ0 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 Bose–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 -