The phenomenon of synchronization in self-sustained systems has been successfully illuminated in many fields, ranging from biology to electrical engineering. To date, the majority of theoretical studies on synchronization focus on isolated self-sustained systems, leaving the effects of surrounding environments less touched due to the lack of appropriate descriptions. Here we derive a generalized Langevin equation that governs the dynamics of open classical Van der Pol (VdP) oscillators immersed in a common thermal bath with arbitrary memory time and subsumes an existing equation for memoryless bath as a special limit. The so-obtained Langevin equation reveals that the bath can induce a dissipative coupling between VdP oscillators, besides the usual damping and thermal noise terms connected by the fluctuation-dissipation theorem. To demonstrate the utility of the approach, we investigate a model system consisting of two open VdP oscillators coupled to a thermal bath with an Ohmic or a Lorentzian-shape spectrum. Unlike the isolated setup where the stable synchronization can be either in-phase or antiphase when varying initial conditions, we find that the bath always favors a single type of synchronization in the long-time limit regardless of initial conditions and the synchronization type can be switched by tuning the temperature. Moreover, we show that the bath-induced dissipative coupling can trigger a synchronization of open VdP oscillators that is otherwise absent between isolated counterparts. Our results complement and extend previous findings for open VdP oscillators.
We show a crossover from coherent to incoherent behavior of charge transport in crystalline organic semiconductors by considering the effect of shallow traps within the dynamical disorder model. The mixed quantum-classical system is treated by the Ehrenfest dynamics method complementing with instantaneous decoherence corrections and energy relaxation, which has been shown to properly make the system close to equilibrium. The shallow traps, which are incorporated by a static diagonal disorder, are shown to play a central role in the crossover. Temperature dependence of charge-carrier mobility is shown to be changed from being negative to positive with the strength of shallow traps increasing, which implies that there is a crossover from hopping to band-like transport. A higher electric field helps to recover the charge-carrier band-like transport behavior from the traps-caused hopping transport. In this way, a unified physical picture of the charge transport in crystalline organic semiconductors is proposed.
To investigate frequency-dependent current noise (FDCN) in open quantum systems at steady states, we present a theory which combines Markovian quantum master equations with a finite time full counting statistics. Our formulation of the FDCN generalizes previous zero-frequency expressions and can be viewed as an application of MacDonald's formula for electron transport to heat transfer. As a demonstration, we consider the paradigmatic example of quantum heat transfer in the context of a non-equilibrium spin-boson model. We adopt a recently developed polaron-transformed Redfield equation which allows us to accurately investigate heat transfer with arbitrary system-reservoir coupling strength, arbitrary values of spin bias, and temperature differences. We observe a turn-over of FDCN in the intermediate coupling regimes, similar to the zero-frequency case. We find that the FDCN with varying coupling strengths or bias displays a universal Lorentzian-shape scaling form in the weak coupling regime, and a white noise spectrum emerges with zero bias in the strong coupling regime due to distinctive spin dynamics. We also find that the bias can suppress the FDCN in the strong coupling regime, in contrast to its zero-frequency counterpart which is insensitive to bias changes. Furthermore, we utilize the Saito-Utsumi relation as a benchmark to validate our theory and study the impact of temperature differences at finite frequencies. Together, our results provide detailed dissections of the finite time fluctuation of heat current in open quantum systems.
To explore energy transfer in the nonequilibrium spin-boson model (NESB) from weak to strong system-bath coupling regimes, we propose a polaron-transformed nonequilibrium Green's function (NEGF) method. By combining the polaron transformation, we are able to treat the system-bath coupling nonperturbatively, thus in direct contrast to conventionally used NEGF methods which take the system-bath coupling as a perturbation. The Majorana-fermion representation is further utilized to evaluate terms in the Dyson series. This method not only allows us to deal with weak as well as strong coupling regimes but also enables an investigation on the role of bias in the energy transfer. As an application of the method, we study an Ohmic NESB. For an unbiased spin system, our energy current result smoothly bridges predictions of two benchmarks, namely, the quantum master equation and the nonequilibrium noninteracting blip approximation, a considerable improvement over existing theories. In case of a biased spin system, we found a bias-induced nonmonotonic behavior of the energy conductance in the intermediate coupling regime, resulting from the resonant character of the energy transfer. This finding may offer a nontrivial quantum control knob over energy transfer at the nanoscale.
Treated traditionally by the Ehrenfest approximation, the dynamics of a one-dimensional molecular crystal model with off-diagonal exciton-phonon coupling is investigated in this work using the Dirac-Frenkel time-dependent variational principle with the multi-D2Ansatz. It is shown that the Ehrenfest method is equivalent to our variational method with the single D2Ansatz, and with the multi-D2Ansatz, the accuracy of our simulated dynamics is significantly enhanced in comparison with the semi-classical Ehrenfest dynamics. The multi-D2Ansatz is able to capture numerically accurate exciton momentum probability and help clarify the relation between the exciton momentum redistribution and the exciton energy relaxation. The results demonstrate that the exciton momentum distributions in the steady state are determined by a combination of the transfer integral and the off-diagonal coupling strength, independent of the excitonic initial conditions. We also probe the effect of the transfer integral and the off-diagonal coupling on exciton transport in both real and reciprocal space representations. Finally, the variational method with importance sampling is employed to investigate temperature effects on exciton transport using the multi-D2Ansatz, and it is demonstrated that the variational approach is valid in both low and high temperature regimes.
We investigate the direct-current response of crystalline organic semiconductors in the presence of finite external electric fields by the quantum-classical Ehrenfest dynamics complemented with instantaneous decoherence corrections (IDC). The IDC is carried out in the real-space representation with the energy-dependent reweighing factors to account for both intermolecular decoherence and energy relaxation by which conduction occurs. In this way, both the diffusion and drift motion of charge carriers are described in a unified framework. Based on an off-diagonal electron-phonon coupling model for pentacene, we find that the drift velocity initially increases with the electric field and then decreases at higher fields due to the Wannier-Stark localization, and a negative electric-field dependence of mobility is observed. The Einstein relation, which is a manifestation of the fluctuation-dissipation theorem, is found to be restored in electric fields up to â¼10(5) V/cm for a wide temperature region studied. Furthermore, we show that the incorporated decoherence and energy relaxation could explain the large discrepancy between the mobilities calculated by the Ehrenfest dynamics and the full quantum methods, which proves the effectiveness of our approach to take back these missing processes.
We explore an instantaneous decoherence correction (IDC) approach for the decoherence and energy relaxation in the quantum-classical dynamics of charge transport in organic semiconducting crystals. These effects, originating from environmental fluctuations, are essential ingredients of the carrier dynamics. The IDC is carried out by measurement-like operations in the adiabatic representation. While decoherence is inherent in the IDC, energy relaxation is taken into account by considering the detailed balance through the introduction of energy-dependent reweighing factors, which could be either Boltzmann (IDC-BM) or Miller-Abrahams (IDC-MA) type. For a non-diagonal electron-phonon coupling model, it is shown that IDC tends to enhance diffusion while energy relaxation weakens this enhancement. As expected, both the IDC-BM and IDC-MA achieve a near-equilibrium distribution at finite temperatures in the diffusion process, while in the Ehrenfest dynamics the electronic system tends to infinite temperature limit. The resulting energy relaxation times with the two kinds of factors lie in different regimes and exhibit different dependences on temperature, decoherence time, and electron-phonon coupling strength, due to different dominant relaxation processes.
We propose a variational approach to study renormalized phonons in momentum-conserving nonlinear lattices with either symmetric or asymmetric potentials. To investigate the influence of pressure for phonon properties, we derive an inequality which provides both the lower and upper bound of the Gibbs free energy as the associated variational principle. This inequality is a direct extension to the Gibbs-Bogoliubov inequality. Taking the symmetry effect into account, the reference system for the variational approach is chosen to be harmonic with an asymmetric quadratic potential which contains variational parameters. We demonstrate the power of this approach by applying it to one-dimensional nonlinear lattices with a symmetric or asymmetric Fermi-Pasta-Ulam-type potential. For a system with a symmetric potential and zero pressure, we recover existing results. For other systems which are beyond the scope of existing theories, including those having symmetric potential and pressure and those having the asymmetric potential with or without pressure, we also obtain accurate sound velocity.
The thermoelectric effects of a single Aharonov-Bohm (SAB) ring and coupled double Aharonov-Bohm (DAB) rings have been investigated on a theoretical basis, taking into account the contributions of both electrons and phonons to the transport process by using the nonequilibrium Green's function technique. The thermoelectric figure of merit of the coupled DAB rings cannot be predicted directly by combining the values of two SAB ring systems due to the contribution of electron-phonon interaction to coupling between the two sites connecting the rings. We find that thermoelectric efficiency can be optimized by modulating the phases of the magnetic flux threading the two rings.
Dynamics of the sub-Ohmic spin-boson model is examined using three numerical approaches, namely the Dirac-Frenkel time-dependent variation with the Davydov D(1) ansatz, the adaptive time-dependent density matrix renormalization group method within the representation of orthogonal polynomials, and a perturbative approach based on a unitary transformation. In order to probe the validity regimes of the three approaches, we study the dynamics of a qubit coupled to a bosonic bath with and without a local field. Comparison of the up-state population evolution shows that the three approaches are in agreement in the weak-coupling regime but exhibit marked differences when the coupling strength is large. The Davydov D(1) ansatz and the time-dependent density matrix renormalization group can both be reliably employed in the weak-coupling regime, while the former is also valid in the strong-coupling regime as judged by how faithfully the trial state follows the Schrödinger equation. We further explore the bipartite entanglement dynamics between two qubits coupled with individual bosonic baths which reveals entanglement sudden death and revival.
The dynamic disorder model for charge carrier transport in organic semiconductors has been extensively studied in recent years. Although it is successful on determining the value of bandlike mobility in the organic crystalline materials, the incoherent hopping, the typical transport characteristic in amorphous molecular semiconductors, cannot be described. In this work, the decoherence process is taken into account via a phenomenological parameter, say, decoherence time, and the projective and Monte Carlo method are applied for this model to determine the waiting time and thus the diffusion coefficient. It is obtained that the type of transport is changed from coherent to incoherent with a sufficiently short decoherence time, which indicates the essential role of decoherence time in determining the type of transport in organics. We have also discussed the spatial extent of carriers for different decoherence time, and the transition from delocalization (carrier resides in about 10 molecules) to localization is observed. Based on the experimental results of spatial extent, we estimate that the decoherence time in pentacene has the order of 1 ps. Furthermore, the dependence of diffusion coefficient on decoherence time is also investigated, and corresponding experiments are discussed.
Within a non-adiabatic dynamical method, we simulate charged polaron motion and dissociation in an organic molecule in the presence of dissipation. The dissipation, represented by damping, is introduced to investigate the influence of temperature on the mobility of carriers. We find that the velocity of the polaron has an inversely linear dependence on the damping, and hence the relationship between mobility and temperature is a power law, which is in agreement with the corresponding experiments. We also find that the velocity of the polaron exhibits a continuous dependence on the electric field in the presence of dissipation. In addition, we find that, in the presence of dissipation, the critical field that dissociates a polaron is reduced.
Chemistry, Physical/methods , Gene Conversion , Algorithms , Carbon/chemistry , Chemistry, Organic/methods , Electrons , Models, Statistical , Molybdenum/chemistry , Organic Chemicals/chemistry , Phonons , Surface Properties , Temperature , Time Factors
By employing an adaptive time-dependent density-matrix-renormalization-group method, we investigate the dynamics of a charged bipolaron in the presence of both electron-phonon and electron-electron interactions. We use a Su-Schrieffer-Heeger model modified to include electron-electron interactions via a Hubbard Hamiltonian, a Brazovskii-Kirova symmetry-breaking term, and an external electric field. Our results show that the velocity of the bipolaron increases first and then decreases with the increasing of the on-site Coulomb interaction, U. Furthermore, the dependence of the bipolaron velocity, bipolaron effective mass, and bipolaron stability on the lattice structures is discussed.
Computer Simulation , Models, Chemical , Polymers/chemistry , Electrons , Time Factors
By employing an adaptive time-dependent density-matrix-renormalization-group method, the spin-flip process of polarons is investigated in a polymer chain with magnetic impurities. Being driven by an external electric field, a polaron carrying both spin 1/2 and charge +/-e moves at a constant speed in the polymer chain. When the polaron passes through a specific site, which couples to a magnetic impurity via spin-exchange interaction, a spin-flip process is observed if its spin is antiparallel to the impurity spin. Our results show that the spin-flip probability is enhanced by the on-site Coulomb interaction and increases with increase in the spin-exchange integral. Additionally, some possible applications of the spin-state swap between the polaron and the impurity are discussed.
The normal modes and the melting character of a bilayer system consisting of binary charged particles with different charge and/or different mass, interacting through a Coulomb potential and confined in a parabolic trap are investigated. The normal mode spectrum is discussed as a function of the charge ratio (CR) and mass ratio (MR) of the two kinds of charged particles as well as the interlayer separation. We show that the dependence of the normal modes on the excited states can be tuned by varying the CR, the MR, and the interlayer distance. Once the interlayer distance is larger than a critical value, the first excited state corresponds only to the intershell rotation mode. In addition, the intershell rotation melting temperature is discussed as a function of the CR and MR as well as the interlayer separation.
OBJECTIVE: To evaluate the accuracy of preoperative magnetic resonance imaging (MRI) with water-bag in rectum in prediction of pathological staging of rectal cancer. METHODS: Clinical data of 19 patients with rectal carcinoma assessed by MRI with water-bag in rectum for tumour (T) and mesorectal nodal (N) staging were analyzed retrospectively. Preoperative MRI assessment was compared with postoperative histopathological findings. RESULTS: The tumors were correctly staged by MRI in 15 patients, understaged in 2 and overstaged in 2. The accuracy of T stage was 78.9% (15/19). Mesorectal node were correctly staged in 11 patients, overstaged in 2 and understaged in 6. The accuracy of node staging was 57.9% (11/19), sensitivity was 3/9, and specificity was 80%(8/10). CONCLUSION: Preoperative MRI with water-bag in rectum can not provide correct predictive data on mesorectal node stage, but has certain value in the T staging of rectal carcinoma.
Magnetic Resonance Imaging/methods , Neoplasm Staging/methods , Rectal Neoplasms/pathology , Adult , Aged , Aged, 80 and over , Female , Humans , Male , Middle Aged , Retrospective Studies
We study the ground-state fidelity and entanglement of a Bose-Fermi mixture loaded in a one-dimensional optical lattice. It is found that the fidelity is able to signal quantum phase transitions between the Luttinger liquid phase, the density-wave phase, and the phase separation state of the system, and the concurrence, as a measure of the entanglement, can be used to signal the transition between the density-wave phase and the Ising phase.
We study the effects of dissipation on photoisomerization (PI). The result suggests the existence of two types of environment depending on whether it entangles with the molecule. With entanglement there is a quantum phase transition between a state where PI persists, to a state where PI is quenched by the environment. Without entanglement, the environment only quantitatively modifies the PI behavior. We discuss the relevance of our results to a recent STM experiment, and predict the signature of the quantum phase transition in optical absorption spectra.
Phonon effects on spin-charge separation in one dimension are investigated through the calculation of one-electron spectral functions in terms of the recently developed cluster perturbation theory together with an optimized phonon approach. It is found that the retardation effect due to the finiteness of phonon frequency suppresses the spin-charge separation and eventually makes it invisible in the spectral function. By comparing our results with experimental data of TTF-TCNQ, it is observed that the electron-phonon interaction must be taken into account when interpreting the angle-resolved photoemission spectroscopy data.
