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  1. Article ; Online: Arnol'd cat map lattices.

    Axenides, Minos / Floratos, Emmanuel / Nicolis, Stam

    Physical review. E

    2023  Volume 107, Issue 6-1, Page(s) 64206

    Abstract: We construct Arnol'd cat map lattice field theories in phase space and configuration space. In phase space we impose that the evolution operator of the linearly coupled maps be an element of the symplectic group, in direct generalization of the case of ... ...

    Abstract We construct Arnol'd cat map lattice field theories in phase space and configuration space. In phase space we impose that the evolution operator of the linearly coupled maps be an element of the symplectic group, in direct generalization of the case of one map. To this end we exploit the correspondence between the cat map and the Fibonacci sequence. The chaotic properties of these systems also can be understood from the equations of motion in configuration space. These describe inverted harmonic oscillators, where the runaway behavior of the potential competes with the toroidal compactification of the phase space. We highlight the spatiotemporal chaotic properties of these systems using standard benchmarks for probing deterministic chaos of dynamical systems, namely, the complete dense set of unstable periodic orbits, which, for long periods, lead to ergodicity and mixing. The spectrum of the periods exhibits a strong dependence on the strength and the range of the interaction.
    Language English
    Publishing date 2023-07-18
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2844562-4
    ISSN 2470-0053 ; 2470-0045
    ISSN (online) 2470-0053
    ISSN 2470-0045
    DOI 10.1103/PhysRevE.107.064206
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  2. Book ; Online: Numerical Simulations of a Spin Dynamics Model Based on a Path Integral Approach

    Nussle, Thomas / Nicolis, Stam / Barker, Joseph

    2023  

    Abstract: Inspired by path integral molecular dynamics, we build a spin model, in terms of spin coherent states, from which we can compute the quantum expectation values of a spin in a constant magnetic field, at finite temperature. This formulation facilitates ... ...

    Abstract Inspired by path integral molecular dynamics, we build a spin model, in terms of spin coherent states, from which we can compute the quantum expectation values of a spin in a constant magnetic field, at finite temperature. This formulation facilitates the description of a discrete quantum spin system in terms of a continuous classical model and recasts the quantum spin effects within the framework of path integrals in a double $1/s$ and $\hbar s$ expansion, where $s$ is the magnitude of the spin. In particular, it allows for a much more direct path to the low- and high-temperature limits of the quantum system and to the definition of effective classical Hamiltonians that describe both thermal and quantum fluctuations. In this formalism, the quantum properties of the spins emerge as an effective anisotropy. We use atomistic spin dynamics to sample the path integral, calculate thermodynamic observables and show that our effective classical models can reproduce the thermal expectation values of the quantum system within temperature ranges relevant for studying magnetic ordering.
    Keywords Condensed Matter - Materials Science ; Physics - Computational Physics
    Subject code 541
    Publishing date 2023-03-01
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  3. Book ; Online: Emerging magnetic nutation

    Thibaudeau, Pascal / Nicolis, Stam

    2021  

    Abstract: Nutation has been recognized as of great significance for spintronics; but justifying its presence has proven to be a hard problem. In this paper we show that nutation can be understood as emerging from a systematic expansion of a kernel that describes ... ...

    Abstract Nutation has been recognized as of great significance for spintronics; but justifying its presence has proven to be a hard problem. In this paper we show that nutation can be understood as emerging from a systematic expansion of a kernel that describes the history of the interaction of a magnetic moment with a bath of colored noise. The parameter of the expansion is the ratio of the colored noise timescale to the precession period. In the process we obtain the Gilbert damping from the same expansion. We recover the known results, when the coefficients of the two terms are proportional to one another, in the white noise limit; and show how colored noise leads to situations where this simple relation breaks down, but what replaces it can be understood by the appropriate generalization of the fluctuation--dissipation theorem. Numerical simulations of the stochastic equations support the analytic approach. In particular we find that the equilibration time is about an order of magnitude longer than the timescale set by the colored noise for a wide range of values of the latter and we can identify the presence of nutation in the non-uniform way the magnetization approaches equilibrium.

    Comment: 7 pages, 2 figures
    Keywords Condensed Matter - Statistical Mechanics ; Condensed Matter - Materials Science ; Condensed Matter - Other Condensed Matter ; High Energy Physics - Theory
    Subject code 612
    Publishing date 2021-03-08
    Publishing country us
    Document type Book ; Online
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  4. Book ; Online: Dynamic magnetostriction for antiferromagnets

    Nussle, Thomas / Thibaudeau, Pascal / Nicolis, Stam

    2019  

    Abstract: In this paper we study the switching properties of the dynamics of magnetic moments, that interact with an elastic medium. To do so we construct a Hamiltonian framework, that can take into account the dynamics in phase space of the variables that ... ...

    Abstract In this paper we study the switching properties of the dynamics of magnetic moments, that interact with an elastic medium. To do so we construct a Hamiltonian framework, that can take into account the dynamics in phase space of the variables that describe the magnetic moments in a consistent way. It is convenient to describe the magnetic moments as bilinears of anticommuting variables that are their own conjugates. However, we show how it is possible to avoid having to deal directly with the anticommuting variables themselves, only using them to deduce non-trivial constraints on the magnetoelastic couplings. We construct the appropriate Poisson bracket and a geometric integration scheme, that is symplectic in the extended phase space and that allows us to study the switching properties of the magnetization, that are relevant for applications, for the case of a toy model for antiferromagnetic NiO, under external stresses. In the absence of magnetoelastic coupling, we recover the results reported in the literature and in our previous studies. In the presence of the magnetoelastic coupling, the characteristic oscillations of the mechanical system have repercussions on the N\'eel order parameter dynamics. This is particularly striking for the spin accumulation which is more than doubled by the coupling to the strain

    here as well, the mechanical oscillations are reflected on the magnetic dynamics. As a consequence of such a stress induced strain, the switching time of the magnetization is slightly faster and the amplitude of the magnetization enhanced.

    Comment: 13 pages, 7 figures
    Keywords Condensed Matter - Materials Science ; Condensed Matter - Strongly Correlated Electrons ; Physics - Computational Physics
    Subject code 531
    Publishing date 2019-07-03
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  5. Book ; Online: Probing magneto-elastic phenomena through an effective spin-bath coupling model

    Nussle, Thomas / Thibaudeau, Pascal / Nicolis, Stam

    2018  

    Abstract: A phenomenological model is constructed, that captures the effects of coupling magnetic and elastic degrees of freedom, in the presence of external, stochastic perturbations, in terms of the interaction of magnetic moments with a bath, whose individual ... ...

    Abstract A phenomenological model is constructed, that captures the effects of coupling magnetic and elastic degrees of freedom, in the presence of external, stochastic perturbations, in terms of the interaction of magnetic moments with a bath, whose individual degrees of freedom cannot be resolved and only their mesoscopic properties are relevant. In the present work, the consequences of identifying the effects of dissipation as resulting from interactions with a bath of spins are explored, in addition to elastic, degrees of freedom. The corresponding stochastic differential equations are solved numerically and the moments of the magnetization are computed. The stochastic equations implicitly define a measure on the space of spin configurations, whose moments at equal times satisfy a hierarchy of deterministic, ordinary differential equations. Closure assumptions are used to truncate the hierarchy and the same moments are computed. We focus on the advantages and problems that each approach presents, for the approach to equilibrium and, in particular, the emergence of longitudinal damping.

    Comment: 20 pages, 3 figure panels. Improved presentation. Version to appear in Eur. Phys. J. B
    Keywords Condensed Matter - Mesoscale and Nanoscale Physics ; Nonlinear Sciences - Chaotic Dynamics ; Physics - Computational Physics
    Subject code 612
    Publishing date 2018-09-16
    Publishing country us
    Document type Book ; Online
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  6. Article ; Online: Long range correlations and folding angle with applications to α-helical proteins.

    Krokhotin, Andrey / Nicolis, Stam / Niemi, Antti J

    The Journal of chemical physics

    2014  Volume 140, Issue 9, Page(s) 95103

    Abstract: The conformational complexity of chain-like macromolecules such as proteins and other linear polymers is much larger than that of point-like atoms and molecules. Unlike particles, chains can bend, twist, and even become knotted. Thus chains might also ... ...

    Abstract The conformational complexity of chain-like macromolecules such as proteins and other linear polymers is much larger than that of point-like atoms and molecules. Unlike particles, chains can bend, twist, and even become knotted. Thus chains might also display a much richer phase structure. Unfortunately, it is not very easy to characterize the phase of a long chain. Essentially, the only known attribute is the radius of gyration. The way how it changes when the degree of polymerization becomes different, and how it evolves when the ambient temperature and solvent properties change, is commonly used to disclose the phase. But in any finite length chain there are corrections to scaling that complicate the detailed analysis of the phase structure. Here we introduce a quantity that we call the folding angle to identify and scrutinize the phase structure, as a complement to the radius of gyration. We argue for a mean-field level relationship between the folding angle and the scaling exponent in the radius of gyration. We then estimate the value of the folding angle in the case of crystallographic α-helical protein structures in the Protein Data Bank. We also show how the experimental value of the folding angle can be obtained computationally, using a semiclassical Born-Oppenheimer description of α-helical chiral chains.
    MeSH term(s) Protein Folding ; Protein Structure, Secondary ; Proteins/chemistry
    Chemical Substances Proteins
    Language English
    Publishing date 2014-03-07
    Publishing country United States
    Document type Journal Article ; Research Support, Non-U.S. Gov't
    ZDB-ID 3113-6
    ISSN 1089-7690 ; 0021-9606
    ISSN (online) 1089-7690
    ISSN 0021-9606
    DOI 10.1063/1.4865933
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  7. Book ; Online: Closing the hierarchy for non-Markovian magnetization dynamics

    Tranchida, Julien / Thibaudeau, Pascal / Nicolis, Stam

    2015  

    Abstract: We propose a stochastic approach for the description of the time evolution of the magnetization of nanomagnets, that interpolates between the Landau--Lifshitz--Gilbert and the Landau--Lifshitz--Bloch approximations, by varying the strength of the noise. ... ...

    Abstract We propose a stochastic approach for the description of the time evolution of the magnetization of nanomagnets, that interpolates between the Landau--Lifshitz--Gilbert and the Landau--Lifshitz--Bloch approximations, by varying the strength of the noise. In addition, we take into account the autocorrelation time of the noise and explore the consequences, when it is finite, on the scale of the response of the magnetization, i.e. when it may be described as colored, rather than white, noise and non-Markovian features become relevant. We close the hierarchy for the moments of the magnetization, by introducing a suitable truncation scheme, whose validity is tested by direct numerical solution of the moment equations and compared to the average deduced from a numerical solution of the corresponding stochastic Langevin equation. In this way we establish a general framework, that allows both coarse-graining simulations and faster calculations beyond the truncation approximation used here.

    Comment: 5 pages LaTeX2e, 2 EPS figures; uses elsarticle.cls. Presented at HMM 2015, 10th International Symposium on Hysteresis Modeling and Micromagnetics
    Keywords Condensed Matter - Statistical Mechanics ; High Energy Physics - Lattice ; Physics - Computational Physics
    Subject code 612 ; 530
    Publishing date 2015-06-01
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  8. Book ; Online: Long range correlations and folding angle in polymers with applications to {\alpha}-helical proteins

    Krokhotin, Andrey / Nicolis, Stam / Niemi, Antti J.

    2013  

    Abstract: The conformational complexity of linear polymers far exceeds that of point-like atoms and molecules. Polymers can bend, twist, even become knotted. Thus they may also display a much richer phase structure than point particles. But it is not very easy to ... ...

    Abstract The conformational complexity of linear polymers far exceeds that of point-like atoms and molecules. Polymers can bend, twist, even become knotted. Thus they may also display a much richer phase structure than point particles. But it is not very easy to characterize the phase of a polymer. Essentially, the only attribute is the radius of gyration. The way how it changes when the degree of polymerization becomes different, and how it evolves when the ambient temperature and solvent properties change, discloses the phase of the polymer. Moreover, in any finite length chain there are corrections to scaling, that complicate the detailed analysis of the phase structure. Here we introduce a quantity that we call the folding angle, a novel tool to identify and scrutinize the phases of polymers. We argue for a mean-field relationship between its values and those of the scaling exponent in the radius of gyration. But unlike in the case of the radius of gyration, the value of the folding angle can be evaluated from a single structure. As an example we estimate the value of the folding angle in the case of crystallographic {\alpha}-helical protein structures in the Protein Data Bank (PDB). We also show how the value can be numerically computed using a theoretical model of {\alpha}-helical chiral homopolymers.

    Comment: 2 figures
    Keywords Physics - Biological Physics ; Condensed Matter - Statistical Mechanics ; Quantitative Biology - Biomolecules
    Subject code 612
    Publishing date 2013-06-22
    Publishing country us
    Document type Book ; Online
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