Noninteracting Model Research Articles

Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems

The generalized Gibbs ensemble (GGE), which involves multiple conserved quantities other than the Hamiltonian, has served as the statistical-mechanical description of the long-time behavior for several isolated integrable quantum systems. The GGE may involve a noncommutative set of conserved quantities in view of the maximum entropy principle, and show that the GGE thus generalized (noncommutative GGE, NCGGE) gives a more qualitatively accurate description of the long-time behaviors than that of the conventional GGE. Providing a clear understanding of why the (NC)GGE well describes the long-time behaviors, we construct, for noninteracting models, the exact NCGGE that describes the long-time behaviors without an error even at finite system size. It is noteworthy that the NCGGE involves nonlocal conserved quantities, which can be necessary for describing long-time behaviors of local observables. We also give some extensions of the NCGGE and demonstrate how accurately they describe the long-time behaviors of few-body observables.

Dissipation engineering of nonreciprocal quantum dot circuits: An input-output approach

Nonreciprocal effects in nanoelectronic devices offer unique possibilities for manipulating electron transport and engineering quantum electronic circuits for information processing purposes. However, a lack of rigorous theoretical tools is hindering this development. Here, we provide a general input-output description of nonreciprocal transport in solid-state quantum dot architectures, based on quantum optomechanical analogs. In particular, we break reciprocity between coherently-coupled quantum dots by dissipation-engineering in which these (so-called) primary dots are mutually coupled to auxiliary, damped quantum dots. We illustrate the general framework in two representative multiterminal noninteracting models, which can be used as building blocks for larger circuits. Importantly, the identified optimal conditions for nonreciprocal behavior hold even in the presence of additional dissipative effects that result from local electron-phonon couplings. Besides the analysis of the scattering matrix, we show that a nonreciprocal coupling induces unidirectional electron flow in the resonant transport regime. Altogether, our analysis provides the formalism and working principles towards the realization of nonreciprocal nanoelectronic devices.

Ultrafast molecular dynamics in terahertz-STM experiments: Theoretical analysis using the Anderson-Holstein model

We analyze ultrafast tunneling experiments in which electron transport through a localized orbital is induced by a single cycle THz pulse. We include both electron-electron and electron-phonon interactions on the localized orbital using the Anderson-Holstein model and consider two possible filling factors, the singly occupied Kondo regime and the doubly occupied regime relevant to recent experiments with a pentacene molecule. Our analysis is based on variational non-Gaussian states and provides the accurate description of the degrees of freedom at very different energies, from the high microscopic energy scales to the Kondo temperature $T_K$. To establish the validity of the new method we apply this formalism to study the Anderson model in the Kondo regime in the absence of coupling to phonons. We demonstrate that it correctly reproduces key properties of the model, including the screening of the impurity spin, formation of the resonance at the Fermi energy, and a linear conductance of $2e^2/h$. We discuss the suppression of the Kondo resonance by the electron-phonon interaction on the impurity site. When analyzing THz STM experiments we compute the time dependence of the key physical quantities, including current, the number of electrons on the localized orbital, and the number of excited phonons. We find long-lived oscillations of the phonon that persist long after the end of the pulse. We compare the results for the interacting system to the non-interacting resonant level model.

Metal-insulator phase transition and topology in a three-component system* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11835011 and 11774316).

Due to the topology, insulators become non-trivial, particularly those with large Chern numbers which support multiple edge channels, catching our attention. In the framework of the tight binding approximation, we study a non-interacting Chern insulator model on the three-component dice lattice with real nearest-neighbor and complex next-nearest-neighbor hopping subjected to Λ- or V-type sublattice potentials. By analyzing the dispersions of corresponding energy bands, we find that the system undergoes a metal–insulator transition which can be modulated not only by the Fermi energy but also the tunable extra parameters. Furthermore, rich topological phases, including the ones with high Hall plateau, are uncovered by calculating the associated band’s Chern number. Besides, we also analyze the edge-state spectra and discuss the correspondence between Chern numbers and the edge states by the principle of bulk-edge correspondence. In general, our results suggest that there are large Chern number phases with C = ± 3 and the work enriches the research about large Chern numbers in multiband systems.

Anomalous dynamics on the ergodic side of the many-body localization transition and the glassy phase of directed polymers in random media

Using the non-interacting Anderson tight-binding model on the Bethe lattice as a toy model for the many-body quantum dynamics, we propose a novel and transparent theoretical explanation of the anomalously slow dynamics that emerges in the bad metal phase preceding the Many-Body Localization transition. By mapping the time-decorrelation of many-body wave-functions onto Directed Polymers in Random Media, we show the existence of a glass transition within the extended regime separating a metallic-like phase at small disorder, where delocalization occurs on an exponential number of paths, from a bad metal-like phase at intermediate disorder, where resonances are formed on rare, specific, disorder dependent site orbitals on very distant generations. The physical interpretation of subdiffusion and non-exponential relaxation emerging from this picture is complementary to the Griffiths one, although both scenarios rely on the presence of heavy-tailed distribution of the escape times. We relate the dynamical evolution in the glassy phase to the depinning transition of Directed Polymers, which results in macroscopic and abrupt jumps of the preferred delocalizing paths when a parameter like the energy is varied, and produce a singular behavior of the overlap correlation function between eigenstates at different energies. By comparing the quantum dynamics on loop-less Cayley trees and Random Regular Graphs we discuss the effect of loops, showing that in the latter slow dynamics and apparent power-laws extend on a very large time-window but are eventually cut-off on a time-scale that diverges at the MBL transition.

Signatures of topology in quantum quench dynamics and their interrelation

Motivated by recent experimental progress in the study of quantum systems far from equilibrium, we investigate the relation between several dynamical signatures of topology in the coherent time-evolution after a quantum quench. Specifically, we study the conditions for the appearance of entanglement spectrum crossings, dynamical quantum phase transitions, and dynamical Chern numbers. For non-interacting models, we show that in general there is no direct relation between these three quantities. Instead, we relate the presence of level crossings in the entanglement spectrum to localized boundary modes that may not be of topological origin in the conventional sense. Finally, we investigate how interactions influence the presence of entanglement spectrum crossings and dynamical quantum phase transitions, by means of time-dependent density matrix renormalization group simulations.

Quantum point contact potential curvature under correlated disorder potentials

We theoretically investigate the curvature of the confinement potential in quantum point contacts (QPCs) under a background disorder potential with Gaussian correlation functions using a noninteracting one-dimensional tight-binding model. The curvature of the potential is evaluated from the gate voltage dependence of the conductance, and the statistical average of the fitting curvature is calculated. The fitting curvature is insensitive to the original QPC confinement curvature when the characteristic length of the QPC potential is larger than the characteristic length of the disorder. In addition, the fitting curvature can be enhanced as the QPC curvature is decreased. Accidental double barrier potential formation on the top of the QPC induces enhancement of the fitting curvature. Finite-temperature effects under the disorder potential are also discussed. Similar results hold in a two-dimensional QPC tight-binding model.

On (non-)dynamical dark energy

The current Universe is composed by a mixture of relativistic species, baryonic matter, dark matter and dark energy which evolve in a non-trivial way at perturbative level. An advanced description of the cosmological dynamics should include non-standard features beyond the simplistic approach idealized by the standard cosmology in which cosmic components do not interact, are adiabatic and dissipationless. We promote a full perturbative analysis of linear scalar perturbations of a non-interacting cosmological model containing baryons, dark matter (both pressureless) and a scalar field allowing for the presence of relative entropic perturbations between the three fluids. Assuming an effective scalar-field sound speed equal to one and neglecting anisotropic stresses we establish a new set of equations for the scalar cosmological perturbations. As a consequence of this new approach, we show that tiny departures from a constant scalar field equation of state $w_S=-1$ damage structure formation in a non-acceptable manner. Hence, by strongly constraining $w_S$ our results provide compelling evidence in favor of the standard cosmological model and rule out a large class of dynamical dark energy models

Simulating time-dependent thermoelectric transport in quantum systems

We put forward a gauge-invariant theoretical framework for studying time-resolved thermoelectric transport in an arbitrary multiterminal electronic quantum system described by a non-interacting tight-binding model. The system is driven out of equilibrium by an external time-dependent electromagnetic field (switched on at time $t_0$) and possibly by static temperature or electrochemical potential biases applied (from the remote past) between the electronic reservoirs. Numerical simulations are conducted by extending to energy transport the wave-function approach developed by Gaury et al. and implemented in the t-Kwant library. We provide a module that allows us to compute the time-resolved heat currents and powers in addition to the (already implemented) charge currents, and thus to simulate dynamical thermoelectric transport through realistic devices, when electron-electron and electron-phonon interactions can be neglected. We apply our method to the non-interacting Resonant Level Model and verify that we recover the results reported in the literature for the time-resolved heat currents in the expected limits. Finally, we showcase the versatility of the library by simulating dynamical thermal transport in a Quantum Point Contact subjected to voltage pulses.

Bounds on the entanglement entropy by the number entropy in non-interacting fermionic systems

Entanglement in a pure state of a many-body system can be characterized by the Rényi entropies S^{(\alpha)}=\ln\textrm{tr}(\rho^\alpha)/(1-\alpha)S(α)=lntr(ρα)/(1−α) of the reduced density matrix \rhoρ of a subsystem. These entropies are, however, difficult to access experimentally and can typically be determined for small systems only. Here we show that for free fermionic systems in a Gaussian state and with particle number conservation, S^{(2)}S(2) can be tightly bound—from above and below—by the much easier accessible Rényi number entropy S^{(2)}_N=-\ln \sum_n p^2(n)SN(2)=−ln∑np2(n) which is a function of the probability distribution p(n)p(n) of the total particle number in the considered subsystem only. A dynamical growth in entanglement, in particular, is therefore always accompanied by a growth—albeit logarithmically slower—of the number entropy. We illustrate this relation by presenting numerical results for quenches in non-interacting one-dimensional lattice models including disorder-free, Anderson-localized, and critical systems with off-diagonal (bond) disorder.

Reentrant s-wave superconductivity in the periodic Anderson model with attractive conduction band Hubbard interaction

Spin-flip scattering from magnetic impurities has a strong pair-breaking effect in s-wave superconductors where increasing the concentration of impurities rapidly destroys superconductivity. For small Kondo temperature TK the destruction of superconductivity is preceded by the reentrant superconductivity at finite temperature range Tc2 < T < Tc1, while the normal phase reappears at T < Tc2 ∼ TK. Here we explore the superconducting phase in a periodic system modeled as the Anderson lattice with additional attractive on-site (Hubbard) interaction g acting on the conduction band electrons. We solve the equations using dynamical mean field theory which incorporates Kondo physics, while the pairing interaction is treated on the static mean-field level. For large coupling g we find reentrant superconductivity which resembles the case with diluted impurities. However, we find evidence that reentrant superconductivity is here not a consequence of many-body correlations leading to the Kondo effect, but it rather stems from a competition between the single-particle hybridization and superconducting pairing. An insight into the spectral functions with in-gap structures is obtained from an approximate noninteracting dual model whose solution interpolates between several exact limits.

Efek Moderasi Size dalam Pengungkapan Sukarela: Bukti Empiris di Bursa Efek Indonesia

The purpose of this study is to analyze the determinants of voluntary disclosure (VD) by using three non-interaction models and one interaction model. This paper observes four VD’s determinants (ownership dispersion, managerial ownership, audit committee, and independent commissioners), one control variable (capital structure), and one moderating variable (total asset). By using panel data analysis (225 observations) on the Indonesia Stock Exchange (IDX), it is found that the total asset can be used as the moderating variable in explaining the determinants of VD in IDX. Furthermore, the interaction model shows better results than non-interaction models. Managerial ownership, independent commissioners, and ownership dispersion show high consistency with the tested hypotheses. This is different from the audit committee which does not support the hypothesis. These findings implicate managerial policies that need to consider good corporate governance in supporting the voluntary disclosure of public companies in Indonesia. Strengthening external validity in the form of replication, developing research models, and refining research methods is needed to strengthen the managerial implications. Testing the robustness by simulating various substitute proxies to optimize the generalization of research findings needs to be considered in future studies.

Surface charge theorem and topological constraints for edge states: Analytical study of one-dimensional nearest-neighbor tight-binding models

For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with nearest-neighbor hoppings and one orbital per site but arbitrary size of the unit cell and generic modulations of on-site potentials and hoppings. The solutions are parametrized by determinants which can be calculated from recursion relations. This representation allows for an elegant analytic continuation to complex quasimomentum consistent with previous treatments for continuum models. Two important analytical results are obtained: (1) An explicit proof of the surface charge theorem is presented including a unique relationship between the boundary charge $Q_B^{(\alpha)}$ of a single band $\alpha$ and the bulk polarization in terms of the Zak-Berry phase with no unknown integer left. This establishes a precise form of a bulk-boundary correspondence relating the {\it boundary charge of a single band} to bulk properties. (2) We derive a topological constraint for the phase-dependence of the edge state energies, where the phase variable describes a continuous shift of the lattice towards the boundary. The topological constraint is shown to be equivalent to the quantization of a topological index $I=\Delta Q_B-\bar{\rho}\in \{-1,0\}$ introduced in an accompanying letter [arXiv:1911.06890]. Here $\Delta Q_B$ is the change of the boundary charge $Q_B$ for a given chemical potential in the insulating regime when the lattice is shifted by one site towards the boundary, and $\bar{\rho}$ is the average charge per site (both in units of the elementary charge $e=1$). This establishes an interesting link between universal properties of the boundary charge and edge state physics discussed within the field of topological insulators.

Logarithmic growth of local entropy and total correlations in many-body localized dynamics

The characterizing feature of a many-body localized phase is the existence of an extensive set of quasi-local conserved quantities with an exponentially localized support. This structure endows the system with the signature logarithmic in time entanglement growth between spatial partitions. This feature differentiates the phase from Anderson localization, in a non-interacting model. Experimentally measuring the entanglement between large partitions of an interacting many-body system requires highly non-local measurements which are currently beyond the reach of experimental technology. In this work we demonstrate that the defining structure of many-body localization can be detected by the dynamics of a simple quantity from quantum information known as the total correlations which is connected to the local entropies. Central to our finding is the necessity to propagate specific initial states, drawn from the Hamiltonian unbiased basis (HUB). The dynamics of the local entropies and total correlations requires only local measurements in space and therefore is potentially experimentally accessible in a range of platforms.

Tailoring metal-insulator transitions and band topology via off-resonant periodic drive in an interacting triangular lattice

A triangular lattice with onsite Coulomb interaction $U$ present only on one sub-lattice, is periodically driven by electromagnetic field with a frequency $\Omega \gg (t,~U)$ at half filling. In this high frequency limit, the electromagnetic vector potential, with an amplitude $A$, modifies the bare hopping and generates new next nearest neighbour hopping parameters. For $U=0$, the driving acts like an emergent intrinsic spin-orbit coupling term and stabilises three dispersive bands with the lower and upper bands having non zero Chern numbers. Within a slave rotor mean field theory, we show that while $U$ freezes out charge fluctuations on the interacting sub-lattice, it does not open up a charge gap without the external drive. In presence of the drive, and small $U$, the system exhibits repeated metal insulator transitions as a function of the amplitude $A$. For large $U$, we establish that the freezing of charge fluctuations on the interacting sub-lattice stabilizes an emergent, low energy \textit{half filled non-interacting Kane-Mele model}, whose band gaps can be tuned by varying $A$. In this limit, we show that the external drive provides an handle to engineer periodic band inversions at specific values of $A$ accompanied by topological phase transitions that are characterised by swapping of band Chern numbers.

One-dimensional model for chemotaxis with hard-core interactions.

In this paper we consider a biased velocity jump process with excluded-volume interactions for chemotaxis, where we account for the size of each particle. Starting with a system of N individual hard rod particles in one dimension, we derive a nonlinear kinetic model using two different approaches. The first approach is a systematic derivation for small occupied fraction of particles based on the method of matched asymptotic expansions. The second approach, based on a compression method that exploits the single-file motion of hard core particles, does not have the limitation of a small occupied fraction but requires constant tumbling rates. We validate our nonlinear model with numerical simulations, comparing its solutions with the corresponding noninteracting linear model as well as stochastic simulations of the underlying particle system.

HPC simulations of brownout: A noninteracting particles dynamic model

Helicopters can experience brownout when flying close to a dusty surface. The uplifting of dust in the air can remarkably restrict the pilot’s visibility area. Consequently, a brownout can disorient the pilot and lead to the helicopter collision against the ground. Given its risks, brownout has become a high-priority problem for civil and military operations. Proper helicopter design is thus critical, as it has a strong influence over the shape and density of the cloud of dust that forms when brownout occurs. A way forward to improve aircraft design against brownout is the use of particle simulations. For simulations to be accurate and comparable to the real phenomenon, billions of particles are required. However, using a large number of particles, serial simulations can be slow and too computationally expensive to be performed. In this work, we investigate an message passing interface (MPI) + graphics processing unit (multi-GPU) approach to simulate brownout. In specific, we use a semi-implicit Euler method to consider the particle dynamics in a Lagrangian way, and we adopt a precomputed aerodynamic field. Here, we do not include particle–particle collisions in the model; this allows for independent trajectories and effective model parallelization. To support our methodology, we provide a speedup analysis of the parallelization concerning the serial and pure-MPI simulations. The results show (i) very high speedups of the MPI + multi-GPU implementation with respect to the serial and pure-MPI ones, (ii) excellent weak and strong scalability properties of the implemented time-integration algorithm, and (iii) the possibility to run realistic simulations of brownout with billions of particles at a relatively small computational cost. This work paves the way toward more realistic brownout simulations, and it highlights the potential of high-performance computing for aiding and advancing aircraft design for brownout mitigation.

THE EFFECT OF LCDS-BASED INTERACTIVE E-SCHOOLBOOK (ESB) AGAINST HOTS AND SCIENTIFIC ATTITUDE OF STUDENTS

This study was aimed to determine the effect of the use of LCDS-based interactive electronic schoolbook (ESB) on atomic nuclei material with a scientific approach to Higher Order Thinking Skill (HOTS) and scientific attitudes of students and to investigate the average HOTS value of students after both using interactive and non-interactive ESB. The research design was a Non-equivalent Control Group Design, involving students as the research subjects from one of the State High Schools in Kotabumi, with XII IPA 5 as an experimental class and XII IPA 4 as a control class. Data processing techniques were performed by T-test. The results of the HOTS pretest-posttest students in the experimental class revealed that the Sig. (2-Tailed) value was smaller than 0.05, which was equal to 0,000, indicating that there was an effect of the use of LCDS-based interactive ESB with a scientific approach to the material of the atomic nuclei on HOTS students. The test results of the differences in scientific attitudes of students between the two classes enclosed that the Sig. (2-Tailed) value of 0.001 was smaller than 0.05. This implied the great influence of the use of LCDS-based interactive ESB on the scientific attitude of students. HOTS results of students in both classes also obtained the Sig. (2-Tailed) value of 0,000, stating that there was a significant difference in the average N-gain HOTS value of students who learned with LCDS-based interactive ESB against the non-interactive model.

Effect of Pelargonidin on carrier recombination lifetime of CTS quantum dots

In the current work, we have prepared stacks of Copper tin sulphide (CTS)/Pelargonidin core/shell quantum dots on soda lime substrates by SILAR technique. Copper tin sulphide quantum dots were of tetragonal phase matching well with JCPDS 089-4714. The absorption coefficient of the core/shell quantum dots increased while the photoluminescence intensity decreased with increasing shell thickness. Decrease of charge carrier confinement energy due to leakage of wavefunction into the shell is the cause of fall in PL intensity. Three transitions were found in all the samples corresponding to 1Se-1Sh, 1Pe-1Ph and 1De-1Dh transitions using the non-interacting particle model. Charge carrier recombination lifetime of P state was found to be in the order of 100 ns, with lifetime increasing with shell thickness, probably due to the P state being the most occupied at room temperature and decrease of surface trap sites with increasing shell thickness. Owing to the high lifetime of CTS/Pelargonidin core/shell quantum dots, these can be used effectively in solar cells where recombination time is a deciding factor for efficiency and also in bioimaging of living cells and tissues.

Phase transitions in Ehrenfest urn model with interactions: Coexistence of uniform and nonuniform states.

A model based on the classic noninteracting Ehrenfest urn model with two urns is generalized to M urns with the introduction of interactions for particles within the same urn. As the inter-particle interaction strength is varied, phases of different levels of nonuniformity emerge and their stabilities are calculated analytically. In particular, coexistence of locally stable uniform and nonuniform phases connected by first-order transition occurs. The phase transition threshold and energy barrier can be derived exactly together with the phase diagram obtained analytically. These analytic results are further confirmed by Monte Carlo simulations.