We study heat transport in a pair of strongly coupled spins. In particular, we present a condition for optimal rectification, i.e., flow of heat in one direction and complete isolation in the opposite direction. We show that the strong-coupling formalism is necessary for correctly describing heat flow in a wide range of parameters, including moderate to low couplings. We present a situation in which the strong-coupling formalism predicts optimal rectification whereas the phenomenological approach predicts no heat flow in any direction, for the same parameter values. [11,12]. It opens perspectives in quantum information processing, motivating studies on light-matter interaction at the single-photon level [13][14][15][16][17]. In analogy to modern electronic circuits, quantum devices have been proposed such as photon diodes [18,19] and photon transistors [20,21]. Diodes are current rectifiers. An optimal rectifier is able to conduct current in one sense and isolate it in the opposite sense.All such realistic quantum systems are, of course, open. Natural atoms interact with electromagnetic environments [22]. Artificial atoms also interact with their solidstate environment. There is the need to understand, at the single-quantum level, for instance, the influence of temperature [23][24][25] and of phonons [26,27], fluctuating charges [28], nuclear or electronic spins [29]. Analogies to diodes and transistors are also extendable to the flow of all such complex excitations [30].Manipulation of individual quantum systems also gave birth to engineered interactions between those systems [31]. In particular, ultra-strong couplings are achieved, e.g., between a two-level system and a single-mode cavity in circuit QED [32], totally modifying standard quantum optical scenarios [33].In this paper, we explore heat transport under the influence of strong coupling between spins. We argue that the strong-coupling formalism is necessary even for moderate and low couplings. We treat a case where optimal rectification is expected within the strong-coupling description and is completely absent for the standard phenomenological approach. Optimal rectification is evidenced by the system of two spins coupled via Ising interaction. A broad range of experiments is capable of reproducing Ising-type interactions, simulating spins in the strong-coupling regime [34].Model. The system of interest consists in a pair of interacting spins. We define the coupling constant ∆ between the spins in the z-direction. The magnetic field h applied to the spin on the left is also in the z-direction. The Hamiltonian of the system isThe spin on the left (right) is coupled with a thermal reservoir at a given temperature T L (T R ). The system is illustrated in Figure 1(a). The four eigenstates of H S are given in terms of the eigenstates of σ, | ↑ and | ↓ , in decreasing energy order for the case of interest, ∆ < h, |4 = | ↑↑ , |3 = | ↑↓ , |2 = | ↓↓ , |1 = | ↓↑ We define the transition frequencies as ω mn = m − n , where k is the eigenvalue of H S for the eig...
We study the flow of energy between a harmonic oscillator (HO) and an external environment consisting of N two-degrees-of-freedom nonlinear oscillators, ranging from integrable to chaotic according to a control parameter. The coupling between the HO and the environment is bilinear in the coordinates and scales with system size as 1/√N. We study the conditions for energy dissipation and thermalization as a function of N and of the dynamical regime of the nonlinear oscillators. The study is classical and based on a single realization of the dynamics, as opposed to ensemble averages over many realizations. We find that dissipation occurs in the chaotic regime for fairly small values of N, leading to the thermalization of the HO and the environment in a Boltzmann distribution of energies for a well-defined temperature. We develop a simple analytical treatment, based on the linear response theory, that justifies the coupling scaling and reproduces the numerical simulations when the environment is in the chaotic regime.
We consider the classical dynamics of two particles moving in harmonic potential wells and interacting with the same external environment HE, consisting of N noninteracting chaotic systems. The parameters are set so that when either particle is separately placed in contact with the environment, a dissipative behavior is observed. When both particles are simultaneously in contact with HE an indirect coupling between them is observed only if the particles are in near-resonance. We study the equilibrium properties of the system considering ensemble averages for the case N=1 and single trajectory dynamics for N large. In both cases, the particles and the environment reach an equilibrium configuration at long times, but only for large N can a temperature be assigned to the system.
Resumo Este trabalho apresenta, por meio do formalismo clássico dos cursos de termodinâmica, um estudo da relação entre a natureza quase estática de um processo termodinâmico e sua reversibilidade. Além disso, a partir dos resultados obtidos ao supor a reversibilidade para um processo termodinâmico composto por um subprocesso fundamentalmente irreversível, exploramos os limites de aplicação das leis da termodinâmica e as nuances contidas nas suas formulações gerais. Consideramos que este artigo possui dois caráteres bem definidos: o didático e o fundamental. O caráter didático fica evidente quando utilizamos as técnicas de cálculo para a extração das quantidades termodinâmicas nos processos infinitesimais e ao colocar o leitor em contato com as técnicas de demonstração por contradição (se uma hipótese leva a uma contradição, ela não pode ser tomada). Ambas as técnicas podem ser vistas como essenciais na abordagem de um número imenso de problemas em Física. Do ponto de vista fundamental, conseguimos evidenciar a íntima relação entre a Primeira e a Segunda leis da Termodinâmica quando lidamos com a determinação das condições de reversibilidade e existência dos processos termodinâmicos.
Estudamos o efeito do acoplamento de um oscilador harmônico a um ambiente externo modelado por N osciladores não-lineares de dois graus de liberdade, cujo regime dinâmico varia, do regular ao caótico, de acordo com um parâmetro de controle. O acoplamento entre o oscilador e o ambiente é bilinear nas coordenadas de cada subsistema e reescala de acordo com o tamanho do ambiente. O foco está centrado nas condições, sobre o número de graus de liberdade e o regime dinâmico dos osciladores não-lineares, para que ocorra a dissipação de energia e termalização do sistema. O trabalho foi desenvolvido num contexto clássico e baseado em um única realização dinâmica, opondo-se à média de ensemble sobre várias realizações. O principal resultado desta tese, é que um ambiente caótico finito, composto por um número razoavelmente pequeno de graus de liberdade, pode simular a ação de um reservatório térmico infinito, dissipando a energia do oscilador a uma taxa exponencial e conduzindo-o à termalização com uma distribuição de Boltzmann para uma temperatura muito bem definida. Baseados na Teoria de Resposta Linear, desenvolvemos um modelo analítico simples que justifica a reescala do acoplamento e reproduz as simulações numéricas quando o ambiente está no regime caótico.
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