Finite-temperature Fluctuations Research Articles

Absolutely Stable Time Crystals at Finite Temperature.

We show that locally interacting, periodically driven (Floquet) Hamiltonian dynamics coupled to a Langevin bath support finite-temperature discrete time crystals (DTCs) with an infinite autocorrelation time. By contrast to both prethermal and many-body localized DTCs, the time crystalline order we uncover is stable to arbitrary perturbations, including those that break the time translation symmetry of the underlying drive. Our approach utilizes a general mapping from probabilistic cellular automata to open classical Floquet systems undergoing continuous-time Langevin dynamics. Applying this mapping to a variant of the Toom cellular automaton, which we dub the "π-Toom time crystal," leads to a 2D Floquet Hamiltonian with a finite-temperature DTC phase transition. We provide numerical evidence for the existence of this transition, and analyze the statistics of the finite temperature fluctuations. Finally, we discuss how general results from the field of probabilistic cellular automata imply the existence of discrete time crystals (with an infinite autocorrelation time) in all dimensions, d≥1.

Thermal spin dynamics of Kitaev magnets: Scattering continua and magnetic field induced phases within a stochastic semiclassical approach

The honeycomb magnet $\alpha-$RuCl$_3$ is a prime candidate material for realizing the Kitaev quantum spin liquid (QSL), but it shows long-range magnetic order at low temperature. Nevertheless, its broad inelastic neutron scattering (INS) response at finite frequency has been interpreted as that of a 'proximate QSL'. A moderate in-plane magnetic field indeed melts the residual zigzag order, giving rise to peculiar intermediate field phases before the high-field polarized state. In INS measurements the low-frequency spin waves disappear, leading to a broad scattering continuum in the field-induced intermediate regime, whose nature is currently under debate. Here, we study the magnetic field dependent spin dynamics of the $K-\Gamma-\Gamma'-$model within a stochastic semiclassical treatment, which incorporates the effect of finite-temperature fluctuations. At temperatures relevant for INS experiments, we show how the excitations of the zigzag phase broaden and that the different intermediate phases all show a similar continuum response. We discuss the implications of our results for experiments and highlight the importance of distinguishing finite temperature fluctuations from genuine quantum fractionalization signatures in frustrated magnets.

Local Kernel Regression and Neural Network Approaches to the Conformational Landscapes of Oligopeptides.

The application of machine learning to theoretical chemistry has made it possible to combine the accuracy of quantum chemical energetics with the thorough sampling of finite-temperature fluctuations. To reach this goal, a diverse set of methods has been proposed, ranging from simple linear models to kernel regression and highly nonlinear neural networks. Here we apply two widely different approaches to the same, challenging problem: the sampling of the conformational landscape of polypeptides at finite temperature. We develop a local kernel regression (LKR) coupled with a supervised sparsity method and compare it with a more established approach based on Behler-Parrinello type neural networks. In the context of the LKR, we discuss how the supervised selection of the reference pool of environments is crucial to achieve accurate potential energy surfaces at a competitive computational cost and leverage the locality of the model to infer which chemical environments are poorly described by the DFTB baseline. We then discuss the relative merits of the two frameworks and perform Hamiltonian-reservoir replica-exchange Monte Carlo sampling and metadynamics simulations, respectively, to demonstrate that both frameworks can achieve converged and transferable sampling of the conformational landscape of complex and flexible biomolecules with comparable accuracy and computational cost.

Critical Role of Thermal Fluctuations for CO Binding on Electrocatalytic Metal Surfaces.

This work considers the evaluation of density functional theory (DFT) when comparing against experimental observations of CO binding trends on the strong binding Pt(111) and intermediate binding Cu(111) and for weak binding Ag(111) and Au(111) surfaces important in electrocatalysis. By introducing thermal fluctuations using appropriate statistical mechanical NVT and NPT ensembles, we find that the RPBE and B97M-rV DFT functionals yield qualitatively better metal surface strain trends and CO enthalpies of binding for Cu(111) and Pt(111) than found at 0 K, thereby correcting the overbinding by 0.2 to 0.3 eV to yield better agreement with the enthalpies determined from experiment. The importance of dispersion effects are manifest for the weak CO binding Ag(111) and Au(111) surfaces at finite temperatures in which the RPBE functional does not bind CO at all, while the B97M-rV functional shows that the CO–metal interactions are a mixture of chemisorbed and physisorbed species with binding enthalpies that are within ∼0.05 eV of experiment. Across all M(111) surfaces, we show that the B97M-rV functional consistently predicts the correct atop site preference for all metals due to thermally induced surface distortions that preferentially favor the undercoordinated site. This study demonstrates the need to fully account for finite temperature fluctuations to make contact with the binding enthalpies from surface science experiments and electrocatalysis applications.

The role of defects and excess surface charges at finite temperature for optimizing oxide photoabsorbers.

Computational screening of materials for solar to fuel conversion technologies has mostly focused on bulk properties, thus neglecting the structure and chemistry of surfaces and interfaces with water. We report a finite temperature study of WO3, a promising anode for photoelectrochemical cells, carried out using first-principles molecular dynamics simulations coupled with many-body perturbation theory. We identified three major factors determining the chemical reactivity of the material interfaced with water: the presence of surface defects, the dynamics of excess charge at the surface, and finite temperature fluctuations of the surface electronic orbitals. These general descriptors are essential for the understanding and prediction of optimal oxide photoabsorbers for water oxidation.

Fluctuations and Topological Defects in Proper Ferroelectric Crystals.

Homotopy theory and first-principles-based effective Hamiltonian simulations are combined to investigate the stability of topological defects in proper ferroelectric crystals. We show that, despite a nearly trivial topology of the order parameter space, these materials can exhibit stable topological point defects in their tetragonal polar phase and stable topological line defects in their orthorhombic polar phase. The stability of such defects originates from a novel mechanism of topological protection related to finite-temperature fluctuations of local dipoles.

Molecular Dynamics Study for Lithium Ion Diffusion in Layered LixCoO2 (x=0.5~1.0)

Diffusion constant of lithium ion is one of the most important properties in cathode materials for lithium ion battery. Various experimental and theoretical approaches have been studied to investigate the diffusion constant in LiCoO2 [1-6]. Lithium vacancy ordering is essential phenomenon to determine the lithium ion dynamics [7, 8] and it is important to understand the relationship between the ordered phase generation and the diffusion constant. In theoretical approach, ab initio calculations using density functional theory (DFT) have been established to evaluate the lithium ion diffusivity in cathodes from lithium hopping model based on activation barrier [4-6]. However, DFT is not appropriate for large simulation including various vacancy configurations because of computational cost explosion. Alternatively, molecular dynamics (MD) is more suitable approach to simulate over ten thousand atoms and MD can directly simulate the lithium diffusion with effective force field. However, generic force field cannot support for variable lithium ion number in LiCoO2 [9-12], because the force field development is difficult under the drastic electronic state changing of cobalt by lithium ion extraction/injection processes. Here, we have improved the force field using embedded atom method to modify the total energies in accordance with amount of neighboring lithium ion. The force field parameters have been optimized to reproduce potential energy surfaces of several lithium diffusion paths estimated by DFT calculations. We also fit vacancy energies and elastic constants at several lithium configurations. In addition, ab initio MD results are used as a reference to reproduce finite temperature fluctuation. For validation, MD simulations in several temperatures were performed. The diffusion constants calculated from mean square displacement of lithium ion were good agreement with experimental results [1, 2] qualitatively. We will talk about microscopic picture of lithium vacancy ordering on that day.

Finite-temperature perturbation theory for the random directed polymer problem

We study the random directed polymer problem—the short-scale behavior of an elastic string (or polymer) in one transverse dimension subject to a disorder potential and finite temperature fluctuations. We are interested in the polymer short-scale wandering expressed through the displacement correlator 〈[δu(X)]2〉, with δu(X) being the difference in the displacements at two points separated by a distance X. While this object can be calculated at short scales using the perturbation theory in higher dimensions d > 2, this approach becomes ill-defined and the problem turns out to be nonperturbative in the lower dimensions and for an infinite-length polymer. In order to make progress, we redefine the task and analyze the wandering of a string of a finite length L. At zero temperature, we find that the displacement fluctuations 〈[δu(X)]2〉 ∝ LX2 depend on L and scale with the square of the segment length X, which differs from a straightforward Larkin-type scaling. The result is best understood in terms of a typical squared angle 〈α2〉 ∝ L, where α = ∂xu, from which the displacement scaling for the segment X follows naturally, 〈[δu(X)]2〉 ∝ 〈α2〉 X2. At high temperatures, thermal fluctuations smear the disorder potential and the lowest-order results for disorder-induced fluctuations in both the displacement field and the angle vanish in the thermodynamic limit L → ∞. The calculation up to the second order allows us to identify the regime of validity of the perturbative approach and provides a finite expression for the displacement correlator, albeit depending on the boundary conditions and the location relative to the boundaries.

Finite-Temperature Micromagnetism

It is investigated how magnetic hysteresis is affected by finite-temperature excitations, using soft regions in hard-magnetic matrices as model systems. In lowest order, magnetization processes are described by the traditional approach of using finite-temperature materials constants such as K1 (T). Nanoscale excitations are usually small perturbations. For example, a Bloch summation over all magnon wave vectors shows that remanence is slightly enhanced, because long-wavelength excitations are suppressed. However, a reverse magnetic field enhances the effect of thermal excitations and causes a small reduction of the coercivity. To describe such effects, we advocate micromagnetic calculations where finite-temperature fluctuations are treated as small corrections to the traditional approach, as contrasted to full-scale Monte Carlo simulations.

Long wavelength gradient drift instability in Hall plasma devices. I. Fluid theory

The problem of long wavelength instabilities in Hall thruster plasmas is revisited. A fluid model of the instabilities driven by the E0×B drift in plasmas with gradients of density, electron temperature, and magnetic field is proposed. It is shown that full account of compressibility of the electron flow in inhomogeneous magnetic field leads to quantitative modifications of earlier obtained instability criteria and characteristics of unstable modes. Modification of the stability criteria due to finite temperature fluctuations is investigated.

Solvent Effects on the Valence UV−Vis Absorption Spectra of Topotecan Anticancer Drug in Aqueous Solution at Room Temperature: A Nanoseconds Time-Scale TD-DFT/MD Computational Study

The low-lying valence electronic excitations of the topotecan anticancer drug, in two stable lactone forms, have been addressed in infinite dilute aqueous solution by combining time-dependent density functional theory calculations with nanoseconds time-scale classical molecular dynamics simulations at 298 K. The effects of the surrounding and fluctuating classical environment on the investigated topotecan forms are included in a perturbed electronic Hamiltonian, which is computed, and then diagonalized, at each frame stored during the molecular dynamics sampling in explicit solution. Current results clearly indicate that, at moderately acidic and physiological conditions, the valence UV-vis absorption spectra of topotecan drug are strongly affected by the surrounding dielectric media and by its perturbing trajectory as arising from finite-temperature fluctuations and supramolecular interactions. Furthermore, the extension of the proposed computational study to hydrated topotecan complexes in liquid water shows that all of the experimentally detected UV-vis spectroscopic features in solution are accurately reproduced only when direct solute-solvent intermolecular interactions are also explicitly taken into account in our simulating scenario. Finally, the present investigation opens up a chance regarding the computational prediction of the UV-vis absorption spectra of topotecan interacting, in silico, with the topoisomerase-DNA binary complex in physiological conditions (i.e., water dilute solution, room temperature).

Anomalous Exciton Condensation in Graphene Bilayers

In ordinary semiconductor bilayers, exciton condensates appear at total Landau-level filling factor nu{T}=1. We predict that similar states will occur in Bernal stacked graphene bilayers at many nonzero integer filling factors. For nu{T}=-3, 1 we find that the superfluid density of the exciton condensate vanishes and that a finite-temperature fluctuation-induced first order isotropic-smectic phase transition occurs when the layer densities are not balanced. These anomalous properties of bilayer graphene exciton condensates are due to the degeneracy of Landau levels with n=0 and n=1 orbital character.

Phosphorylation Reaction in cAPK Protein Kinase-Free Energy Quantum Mechanical/Molecular Mechanics Simulations

We present results of a theoretical analysis of the phosphorylation reaction in cAMP-dependent protein kinase using a combined quantum mechanical and molecular mechanics (QM/MM) approach. Detailed analysis of the reaction pathway is provided using a novel QM/MM implementation of the nudged elastic band method, finite temperature fluctuations of the protein environment are taken into account using free energy calculations, and an analysis of hydrogen bond interactions is performed on the basis of calculated frequency shifts. The late transfer of the substrate proton to the conserved aspartate (D166), the activation free energy of 15 kcal/mol, and the slight exothermic (-3 kcal/mol) character of the reaction are all consistent with the experimental data. The near attack conformation of D166 in the reactant state is maintained by interactions with threonine-201, asparagine-177, and most notably by a conserved water molecule serving as a strong structural link between the primary metal ion and the D166. The secondary Mg ion acts as a Lewis acid, attacking the beta-gamma bridging oxygen of ATP. This interaction, along with a strong hydrogen bond between the D166 and the substrate, contributes to the stabilization of the transition state. Lys-168 maintains a hydrogen bond to a transferring phosphoryl group throughout a reaction process. This interaction increases in the product state and contributes to its stabilization.

Probing irradiation induced DNA damage mechanisms using excited state Car-Parrinello molecular dynamics

Photoinduced proton transfer in the Watson-Crick guanine (G)-cytosine (C) base pair has been studied using Car-Parrinello molecular dynamics (CP-MD). A flexible mechanical constraint acting on all three hydrogen bonds in an unbiased fashion has been devised to explore the free energy profile along the proton transfer coordinate. The lowest barrier has been found for proton transfer from G to C along the central hydrogen bond. The resulting charge transfer excited state lies energetically close to the electronic ground state suggesting the possibility of efficient radiationless decay. It is found that dynamic, finite temperature fluctuations significantly reduce the energy gap between the ground and excited states for this charge transfer product, promoting the internal conversion process. A detailed analysis of the internal degrees of freedom reveals that the energy gap is considerably reduced by out-of-plane molecular vibrations, in particular. Consequently, it appears that considering only the minimum energy path provides an upper-bound estimate of the associated energy gap compared to the full-dimension dynamical reaction coordinate. Furthermore, the first CP-MD simulations of the G-C base pair in liquid water are presented, and the effects of solvation on its electronic structure are analyzed.

Role of protein frame and solvent for the redox properties of azurin from Pseudomonas aeruginosa

We have coupled hybrid quantum mechanics (density functional theory; Car-Parrinello)/molecular mechanics molecular dynamics simulations to a grand-canonical scheme, to calculate the in situ redox potential of the Cu(2+) + e(-) --> Cu(+) half reaction in azurin from Pseudomonas aeruginosa. An accurate description at atomistic level of the environment surrounding the metal-binding site and finite-temperature fluctuations of the protein structure are both essential for a correct quantitative description of the electronic properties of this system. We report a redox potential shift with respect to copper in water of 0.2 eV (experimental 0.16 eV) and a reorganization free energy lambda = 0.76 eV (experimental 0.6-0.8 eV). The electrostatic field of the protein plays a crucial role in fine tuning the redox potential and determining the structure of the solvent. The inner-sphere contribution to the reorganization energy is negligible. The overall small value is mainly due to solvent rearrangement at the protein surface.

Bloch oscillations in a homogeneous nucleotide chain

It is shown that, at zero temperature, a hole placed in a homogeneous synthetic nucleotide chain with applied electric field demonstrates Bloch oscillations. The oscillations of the hole placed initially on one of the base pairs arise in response to disruption of the initial charge distribution caused by nucleotide vibrations. The finite temperature fluctuations result in degradation of coherent oscillations. The maximum permissible temperature for DNA “Bloch oscillator” occurrence is estimated.

Thermal fluctuations of induced fermion number

We analyze the phenomenon of induced fermion number at finite temperature. At finite temperature, the induced fermion number $〈N〉$ is a thermal expectation value, and we compute the finite temperature fluctuations $(\ensuremath{\Delta}{N)}^{2}=〈{N}^{2}〉\ensuremath{-}〈N{〉}^{2}.$ While the zero temperature induced fermion number is topological and is a sharp observable, the finite temperature induced fermion number is generically nontopological, and is not a sharp observable. The fluctuations are due to the mixing of states inherent in any finite temperature expectation value. We analyze in detail two different cases in $(1+1)$-dimensional field theory: fermions in a kink background, and fermions in a chiral sigma model background. At zero temperature the induced fermion numbers for these two cases are very similar, but at finite temperature they are very different. The sigma model case is generic and the induced fermion number is nontopological, but the kink case is special and the fermion number is topological, even at finite temperature. There is a simple physical interpretation of all these results in terms of the spectrum of the fermions in the relevant background, and many of the results generalize to higher dimensional models.

On Entropic Reduction of Fluctuations

We point out that there is no general relation between ground state degeneracy and finite-temperature fluctuations for tilted interfaces.

First-principles investigations of atomic disorder effects on magnetic and structural instabilities in transition-metal alloys.

In this paper we use the coherent-potential approximation within the Korringa-Kohn-Rostocker band-structure scheme to investigate the influence of atomic disorder on magnetism and crystal structure of transition-metal alloys like iron-nickel. This method allows an investigation of disordered alloys on an equally well-defined basis as an investigation of corresponding stoichiometrically ordered phases. In particular we have calculated the magnetic and structural binding surfaces of fcc ${\mathrm{Fe}}_{\mathit{x}}$${\mathrm{Ni}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$ for concentrations close to the critical concentration x=0.65 which corresponds to the Invar alloy ${\mathrm{Fe}}_{65}$${\mathrm{Ni}}_{35}$, with the help of the fixed-spin-moment method. We find that magnetism in the ground state gradually vanishes as we go from ${\mathrm{Fe}}_{60}$${\mathrm{Ni}}_{40}$, which has a well-defined magnetic ground state being separated from the nonmagnetic state by 1.0 mRy/atom, to ${\mathrm{Fe}}_{75}$${\mathrm{Ni}}_{25}$ which is nonmagnetic. The criical concentration for which this disorder driven magnetic-nonmagnetic transition occurs is x\ensuremath{\approxeq}0.65--0.70 in accordance with the magnetic phase diagram of ${\mathrm{Fe}}_{\mathit{x}}$${\mathrm{Ni}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$. These calculations have to be compared with ab initio calculations for ordered fcc ${\mathrm{Fe}}_{3}$Ni; here the magnetic ground state is by 1.25 mRy more stable than the nonmagnetic state. This different magnetic behavior of disordered and ordered phases can be explained on statistical grounds. Furthermore, the magnetic disordered ground state is unstable with respect to a martensitic fcc\ensuremath{\rightarrow}bcc transition on the Fe-rich side in accordance with the structural phase diagram of ${\mathrm{Fe}}_{\mathit{x}}$${\mathrm{Ni}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$. We have furthermore calculated the temperature evolution of the binding surfaces with the help of a finite-temperature fluctuation theory. We find interesting reentrant ferromagnetic phase transitions in the fcc phase close to the Invar concentration x=0.65.

Fluctuation effects in ultrathin films

We discuss finite temperature fluctuations of the magnetization M in ultrathin magnetic films where spins interact with short-range exchange (J), anisotropy (K) and long-range dipolar (g) couplings. Phase boundaries for a triangular lattice are obtained from Monte Carlo simulations as a function of J, g and K. For nonzero g, the magnetization can rotate from the z to the in-plane direction. The transition temperature as a function of the effective anisotropy field K − g/0.1208 is essentially unchanged as g becomes zero. This suggests a new physical picture in which, as the temperature is increased, the change in the direction of M for g ≠ 0 is closely connected with the Ising transition for g = 0 when the Mz disappears. Mean field calculations suggest three transitions where only Mz is finite at low temperature. As the temperature is increased, (1) Mx becomes nonzero, (2) Mz becomes zero and eventually (3) Mx becomes zero.