Finite Chain Research Articles

What is Multi-extreme THz ESR? Developments and its Applications

AbstractThis review explores the multi-extreme THz ESR system in Kobe, Japan, with a focus on pulsed magnetic fields, mechanical detection, and high pressure as central elements of multi-extreme THz ESR. Initially, it discusses the advantages of multi-frequency THz ESR using mini-pulsed and 55 T‒pulsed magnetic fields, with typical examples featuring the finite Haldane chain substance Y2BaNi0.96Mg0.04O5 and the deformed diamond chain antiferromagnet Cu3(CO3)2(OH)2 (Azurite). The measurement efficiency and the measurement beyond the magnetic phase transition, in contrast to the conventional superconducting magnet, are discussed. Second, the high sensitivity obtained from the use of a nano-membrane for mechanical detection is shown. Also shown are the high-temperature (280 K) THz ESR results for DPPH powder and a Cu(C4H4N2)(NO3)2 (CuPzN) single crystal, with the combination of a nano-membrane device and a high-power source, a gyrotron. Finally, the high-pressure THz ESR results for KCuCl3 using a transmission-type double-layered pressure cell are shown, along with the application of the thermally detected high-pressure THz ESR.

Generalized hydrodynamics and approach to generalized Gibbs equilibrium for a classical harmonic chain

Abstract We study the evolution of a classical harmonic chain with nearest-neighbor interactions starting from domain wall initial conditions. The initial state is taken to be either a product of two Gibbs ensembles (GEs) with unequal temperatures on the two halves of the chain or a product of two generalized Gibbs ensembles (GGEs) with different parameters in the two halves. For this system, we construct the Wigner function and demonstrate that its evolution defines the generalized hydrodynamics (GHD) describing the evolution of the conserved quantities. We solve the GHD for both finite and infinite chains and compute the evolution of conserved densities and currents. For a finite chain with fixed boundaries, we show that these quantities relax as ∼ 1 / t to their respective steady-state values given by the final expected GE or GGE state, depending on the initial conditions. Exact expressions for the Lagrange multipliers of the final expected GGE state are obtained in terms of the steady-state densities. In the case of an infinite chain, we find that the conserved densities and currents at any finite time exhibit ballistic scaling while, at infinite time, any finite segment of the system can be described by a current-carrying non-equilibrium steady state (NESS). We compute the scaling functions analytically and show that the relaxation to the NESS occurs as ∼ 1 / t for the densities and as ∼ 1 / t 2 for the currents. We compare the analytical results from hydrodynamics with those from exact microscopic numerics and find excellent agreement.

Robust theory of thermal activation in magnetic systems with Gilbert damping

Magnetic systems can exhibit thermally activated transitions whose timescales are often described by an Arrhenius law. However, robust predictions of such timescales are only available for certain cases. Inspired by the harmonic theory of Langer, we derive a general activation rate for multidimensional spin systems. Assuming local thermal equilibrium in the initial minimum and deriving an expression for the flow of probability density along the unstable dynamical mode at the saddle point, we obtain the expression for the activation rate that is a function of the Gilbert damping parameter, α. We find that this expression remains valid for the physically relevant regime of α≪1. When the activation is characterized by a coherent reorientation of all spins, we gain insight into the prefactor of the Arrhenius law by writing it in terms of spin wave frequencies and, for the case of a finite spin chain, obtain an expression that depends exponentially on the square of the system size indicating a break-down of the Meyer-Neldel rule. Published by the American Physical Society 2024

Extracting Thermodynamic Properties of Carbyne from Tip-Enhanced Raman Scattering Images.

The measurement of thermodynamic properties for nanosystems is essential to comprehend the inherent characteristics of nanomaterials. Traditional spectroscopy measurements, such as Raman or ultraviolet-visible spectroscopies, are limited to offering insights near the Γ point in the Brillouin zone and thus cannot precisely determine the system's thermodynamic properties, for example, heat capacity. Utilizing the intrinsic broad momentum distribution in highly confined plasmonic fields, here we take sp-hybridized carbyne as a proof-of-the-principle example to show that ultrahigh-resolution tip-enhanced Raman scattering (TERS) images have the ability to access all k-points in the phonon Brillouin zone of one-dimensional nanosystems, allowing the comprehensive determination of vibrational features and heat capacity for finite carbon chains. Comparing phonon dispersion spectra and heat capacities under different boundary conditions, i.e., linear carbon chains and cyclic carbon molecules, we find that the heat capacities of linear structures converge more rapidly than the counterparts of cyclic structures to the benchmark of ideal carbyne. We also study the effects of different terminal groups in linear structures as well as the aromaticity in cyclic structures on heat capacity. This study provides a practical method for characterizing the thermodynamic properties of nanosystems, demonstrating the potential applications of TERS imaging in nanomaterial science.

Finite Time Path Field Theory Perturbative Methods for Local Quantum Spin Chain Quenches

We discuss local magnetic field quenches using perturbative methods of finite time path field theory (FTPFT) in the following spin chains: Ising and XY in a transverse magnetic field. Their common characteristics are: (i) they are integrable via mapping to a second quantized noninteracting fermion problem; and (ii) when the ground state is nondegenerate (true for finite chains except in special cases), it can be represented as a vacuum of Bogoliubov fermions. By switching on a local magnetic field perturbation at finite time, the problem becomes nonintegrable and must be approached via numeric or perturbative methods. Using the formalism of FTPFT based on Wigner transforms (WTs) of projected functions, we show how to: (i) calculate the basic “bubble” diagram in the Loschmidt echo (LE) of a quenched chain to any order in the perturbation; and (ii) resum the generalized Schwinger–Dyson equation for the fermion two-point retarded functions in the “bubble” diagram, hence achieving the resummation of perturbative expansion of LE for a wide range of perturbation strengths under certain analyticity assumptions. Limitations of the assumptions and possible generalizations beyond it and also for other spin chains are further discussed.

A presentation for the semigroup of order-preserving full contraction mappings of a finite chain

For n ∈ Z + , let X n = { 1 , … , n } be a finite chain and T n be the full transformation semigroup on Xn . If O C T n is the set of all order-preserving and full contraction mappings on Xn , then it is well-known that O C T n is a submonoid of T n . In this paper we give a monoid presentation of O C T n .

Risk conscious investment

The risk conscious investor is defined as the maximizer of a conservative valuation or a dynamic nonlinear expectation. Both the static and dynamic problems are addressed using distortions of tail probabilities or distortions of tail measures. The multivariate static problem is solved in the context of the multivariate bilateral gamma model. For the dynamic model states and their transitions are modeled in two ways. The first defines states by a parametric model for the return distribution with transitions described by a continuous-time finite state Markov chain between the distributional possibilities. In the second model states are represented by the first four power variations with transitions given by (OU) equations for modeling stochastically the first four power variations as Tempered Fractional Lévy Processes (TFLP). Numerical solutions for policy functions are implemented in trading 768 equity assets over seven years ending December 2021.

On the kinetic temperature of a one-dimensional crystal on the long-time scale

We investigate the dynamics of the kinetic temperature of a finite one-dimensional harmonic chain, the evolution of which is initiated by a thermal shock. We demonstrate that the kinetic temperature returns arbitrarily close to its initial state (the one immediately following the thermal shock) infinitely many times, and we give an estimate for the time elapsed until the recurrence. This assertion is closely related to the Poincare recurrence theorem and we discuss their relation. To estimate the recurrence time we use its averaging along system’s trajectory and provide a rigorous mathematical definition of the mean recurrence time. It turns out that the mean recurrence time exponentially increases with the number of particles in the chain. A connection is established between this problem and the local theorems of large deviations theory.Previous studies have shown that in such a one-dimensional harmonic chain, at times of order N, a thermal echo phenomenon is observed — a sharp increase in the amplitude of kinetic temperature fluctuations. In the present work, we give a rigorous mathematical formulation to this phenomenon and estimate the amplitude of the fluctuations.The research is funded by the Ministry of Science and Higher Education of the Russian Federation within the framework of the Research Center of World-Class Program: Advanced Digital Technologies (agreement №075-15-2020-311 dated 04.20.2022).

Environment-mediated long-ranged correlations in many-body system

Quantum states in complex aggregates are unavoidably affected by environmental effects, which typically cannot be accurately modeled by simple Markovian processes. As system sizes scale up, nonperturbative simulation becomes thus unavoidable, but they are extremely challenging due to the intimate interplay of intrinsic many-body interaction and time-retarded feedback from environmental degrees of freedom. In this work, we utilize the recently developed quantum dissipation with minimally extended state space approach to address reservoir induced long-ranged temporal correlations in finite size Ising-type spin chains. For thermal reservoirs with ohmic and subohmic spectral density, we simulate the quantum time evolution from finite to zero temperature. The competition between thermal fluctuations, quantum fluctuations, and anti-/ferromagnetic interactions reveals a rich pattern of dynamical phases, including dissipative induced phase transitions and spatiotemporal correlations.

Exponentially localized interface eigenmodes in finite chains of resonators

AbstractThis paper studies wave localization in chains of finitely many resonators. There is an extensive theory predicting the existence of localized modes induced by defects in infinitely periodic systems. This work extends these principles to finite‐sized systems. We consider one‐dimensional, finite systems of subwavelength resonators arranged in dimers that have a geometric defect in the structure. This is a classical wave analog of the Su–Schrieffer–Heeger model. We prove the existence of a spectral gap for defectless finite dimer structures and find a direct relationship between eigenvalues being within the spectral gap and the localization of their associated eigenmode. Then, for sufficiently large‐size systems, we show the existence and uniqueness of an eigenvalue in the gap in the defect structure, proving the existence of a unique localized interface mode. To the best of our knowledge, our method, based on Chebyshev polynomials, is the first to characterize quantitatively the localized interface modes in systems of finitely many resonators.

Political institutions and output collapses

This paper examines whether major output collapses are more likely under autocracy. Using data on 123 developing countries over 1971–2016, we model the joint evolution of output growth and political institutions as a finite state Markov chain with a two-dimensional state space. We study how countries move between states. We find that growth is more likely to be sustained under democracy than under autocracy; output collapses are more likely to deepen under autocracy; and stagnation under autocracy can give way to outright collapse. Democratic countries appear to be more resilient.

Cooperative Decay of an Ensemble of Atoms in a One-Dimensional Chain with a Single Excitation

We propose a new expression of the cooperative decay rate of a one-dimensional chain of N two-level atoms in the single-excitation configuration. From it, the interference nature of superradiance and subradiance arises naturally, without the need to solve the eigenvalue problem of the atom–atom interaction Green function. The cooperative decay rate can be interpreted as the imaginary part of the expectation value of the effective non-Hermitian Hamiltonian of the system, evaluated over a generalized Dicke state of N atoms in the single-excitation manifold. Whereas the subradiant decay rate is zero for an infinite chain, it decreases as 1/N for a finite chain. A simple approximated expression for the cooperative decay rate is obtained as a function of the lattice constant d and the atomic number N. The results are obtained first for the scalar model and then extended to the vectorial light model, assuming all the dipoles aligned.

On the monoid of order-preserving transformations of a finite chain whose ranges are intervals

AbstractWe give a presentation for the monoid $$\mathscr{I}\mathscr{O}_n$$ I O n of all order-preserving transformations of an n-chain whose ranges are intervals. We also consider the submonoid $$\mathscr{I}\mathscr{O}_n^-$$ I O n - of $$\mathscr{I}\mathscr{O}_n$$ I O n consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.

Quantum design of magnetic structures with enhanced magnetocaloric properties

Abstract The magnetization processes and magnetocaloric effect (MCE) of molecular magnets are studied using the quantum Heisenberg model with the goal of finding magnetic structures with optimal magnetocaloric properties. To fulfill this goal, we examine the influence of various factors such as quantum fluctuations, the magnitude and distribution of spins, the cluster size and its geometry on the conventional (cooling) and inverse (heating) MCE. We find, surprisingly, that the best cooling and heating effects are observed in the Ising limit on the smallest possible molecular clusters represented by dimers and trimers. The increasing Heisenberg interaction suppresses both the cooling as well as heating effects, but while the heating is reduced very strongly, for relatively small values of the anisotropic Heisenberg constant, the cooling effects are reduced only weakly. Since the heating effect is undesired in low-temperature refrigeration, the Heisenberg limit is also interesting from a practical point of view. Moreover, we find that spin distributions also have a significant influence on the magnetocaloric properties of molecular magnets. Specifically, configurations with large spins on the edges of the finite chain significantly enhance the cooling effect.

Self dual and MHDR dual cyclic codes over finite chain rings

Self dual and MHDR dual cyclic codes over finite chain rings

Metastable Γ-expansion of finite state Markov chains level two large deviations rate functions

Metastable Γ-expansion of finite state Markov chains level two large deviations rate functions

Comparative analysis of absorption resonances between carbynes and cyclo [n] carbons

Two approaches are presented here to analyze the absorption resonances between carbynes and cyclo [n] carbons, namely the analytical tight-binding model to calculate the optical selection rules of cumulenic atomic rings and chains and the ab initio time-dependent density functional theory for the optical investigation of polyynic carbon ring and chains. The optical absorption spectra of the carbon ring match that of the finite chain when their eigen energies align following the Nring=2Nchain+2 rule, which states that the number of atoms in an atomic ring Nring is twice the number of atoms on a finite chain Nchain with two additional atoms. Two representative atomic chains are chosen for our numerical calculations, specifically carbynes with N=7and8 carbon atoms as optical resonance spectra match to a recently synthesized carbon ring called cyclo[18]carbon. Despite the mismatch in resonance peaks, molecular orbital transitions of both carbynes N = 7 and 8 and cyclo[18]carbon reveal a wave function symmetry change from inversion to reflection and vice versa for allowed molecular orbital transitions, which results in electron density redistribution along the polyynic carbyne axis or the cyclo[18]carbon circumference. Our investigation of the correlation of optical absorption peaks between carbynes and cyclo [n] carbons is a step towards enhancing the reliability of allotrope identification in advanced molecular device spectroscopy. Moreover, this work could facilitate the non-invasive, rapid and crucial assessment of these sensitive 1D allotropes by providing accurate descriptions of their electronic and optical properties, particularly in controlled synthesis environments.

On a class of constacyclic codes of length 4ps over 𝔽pm[u] 〈u3〉

Let [Formula: see text] be a prime such that [Formula: see text], where [Formula: see text] is a positive integer. For any nonzero element [Formula: see text] of [Formula: see text], we determine the algebraic structure of all [Formula: see text]-constacyclic codes of length [Formula: see text] over the finite commutative chain ring [Formula: see text], where [Formula: see text] and [Formula: see text] is a positive integer. If the unit [Formula: see text] is a square, [Formula: see text], each [Formula: see text]-constacyclic code of length [Formula: see text] is expressed as a direct sum of an [Formula: see text]-constacyclic code and an [Formula: see text]- constacyclic code of length [Formula: see text]. In the main case that the unit [Formula: see text] is not a square, it is shown that any nonzero polynomial of degree at most [Formula: see text] over [Formula: see text] is invertible in the ambient ring [Formula: see text]. It is also proven that the ambient ring [Formula: see text] is a local ring with the unique maximal ideal [Formula: see text], where [Formula: see text]. Such [Formula: see text]-constacyclic codes are then classified into eight distinct types of ideals, and the detailed structures of ideals in each type are provided. Among other results, the number of codewords, and the dual of each [Formula: see text]-constacyclic code are obtained. The non-existence of self-dual and isodual [Formula: see text]-constacyclic codes of length [Formula: see text] over [Formula: see text], when the unit [Formula: see text] is not a square, is likewise proved.

Enumeration formulae for self-orthogonal, self-dual and complementary-dual additive cyclic codes over finite commutative chain rings

Enumeration formulae for self-orthogonal, self-dual and complementary-dual additive cyclic codes over finite commutative chain rings

Reliability analysis and preventive maintenance policy for consecutive k$k$‐out‐of‐n:F$n: F$ balanced system under failure criterion operating in shock environment

AbstractThis paper presents a consecutive ‐out‐of‐: balance system in a shock environment, where the state transition of component is induced by external shocks. If a predetermined threshold number of effective shocks are applied to component in a critical state, the component will fail. The state of the system is defined by the number of consecutive failing component groups in the system, which leads to system failure when a critical number of consecutive failing components is reached. To minimize maintenance costs, we propose a preventive maintenance method with an optimization model. We use finite Markov chain imbedding and Phase‐type distribution to calculate component group failure rates and associated probability functions in discrete and continuous time, respectively. The validity and accuracy of the model are confirmed by numerical examples and Monte Carlo simulations.