Two-body Dissipation Research Articles

Random two-body dissipation induced non-Hermitian many-body localization

<sec>Recent researches on disorder-driven many-body localization (MBL) in non-Hermitian quantum systems have aroused great interest. In this work, we investigate the non-Hermitian MBL in a one-dimensional hard-core Bose model induced by random two-body dissipation, which is described by</sec><sec> <inline-formula><tex-math id="M1">\begin{document}$ \hat{H}=\displaystyle\sum\limits_{j}^{L-1}\left[ -J\left( \hat{b}_{j}^{\dagger}\hat{b}_{j+1}+\hat {b}_{j+1}^{\dagger}\hat{b}_{j}\right) +\frac{1}{2}\left( U-{\mathrm{i}}\gamma_{j}\right) \hat{n}_{j}\hat{n}_{j+1}\right] \notag,$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M1.png"/></alternatives></inline-formula> </sec><sec>with the random two-body loss <inline-formula><tex-math id="M2">\begin{document}$\gamma_j\in\left[0,W\right]$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M2.png"/></alternatives></inline-formula>. By the level statistics, the system undergoes a transition from the AI<inline-formula><tex-math id="M3">\begin{document}$^{\dagger}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M3.png"/></alternatives></inline-formula> symmetry class to a two-dimensional Poisson ensemble with the increase of disorder strength. This transition is accompanied by the changing of the average magnitude (argument) <inline-formula><tex-math id="M4">\begin{document}$\overline{\left\langle {r}\right\rangle}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M4.png"/></alternatives></inline-formula> (<inline-formula><tex-math id="M5">\begin{document}$\overline{-\left\langle \cos {\theta}\right\rangle }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M5.png"/></alternatives></inline-formula>) of the complex spacing ratio, shifting from approximately 0.722 (0.193) to about 2/3 (0). The normalized participation ratios of the majority of eigenstates exhibit finite values in the ergodic phase, gradually approaching zero in the non-Hermitian MBL phase, which quantifies the degree of localization for the eigenstates. For weak disorder, one can see that average half-chain entanglement entropy <inline-formula><tex-math id="M8">\begin{document}$\overline{\langle S \rangle}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M8.png"/></alternatives></inline-formula> follows a volume law in the ergodic phase. However, it decreases to a constant independent of <i>L</i> in the deep non-Hermitian MBL phase, adhering to an area law. These results indicate that the ergodic phase and non-Hermitian MBL phase can be distinguished by the half-chain entanglement entropy, even in non-Hermitian system, which is similar to the scenario in Hermitian system. Finally, for a short time, the dynamic evolution of the entanglement entropy exhibits linear growth with the weak disorder. In strong disorder case, the short-time evolution of <inline-formula><tex-math id="M9">\begin{document}$\overline{S(t)}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M9.png"/></alternatives></inline-formula> shows logarithmic growth. However, when <inline-formula><tex-math id="M10">\begin{document}$t\geqslant10^2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M10.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M11">\begin{document}$\overline{S(t)}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M11.png"/></alternatives></inline-formula> can stabilize and tend to the steady-state half-chain entanglement entropy <inline-formula><tex-math id="M12">\begin{document}$\overline{ S_0 }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M12.png"/></alternatives></inline-formula>. The results of the dynamical evolution of <inline-formula><tex-math id="M13">\begin{document}$\overline{S(t)}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M13.png"/></alternatives></inline-formula> imply that one can detect the occurrence of the non-Hermitian MBL by the short-time evolution of <inline-formula><tex-math id="M14">\begin{document}$\overline{S(t)}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M14.png"/></alternatives></inline-formula>, and the long-time behavior of <inline-formula><tex-math id="M15">\begin{document}$\overline{S(t)}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231987_M15.png"/></alternatives></inline-formula> signifies the steady-state information.</sec>

Non-Hermitian Haldane-Hubbard model: Effective description of one- and two-body dissipation

Non-Hermitian Haldane-Hubbard model: Effective description of one- and two-body dissipation

Binary formation through gas-assisted capture and the implications for stellar, planetary, and compact object evolution

ABSTRACTBinary systems are ubiquitous and their formation requires two-body interaction and dissipation. In gaseous media, interactions between two initially unbound objects could result in gas-assisted binary formation, induced by a loss of kinetic energy to the ambient gas medium. Here, we derive analytically the criteria for gas-assisted binary capture through gas dynamical friction dissipation. We validate them with few-body simulations and explore this process in different gas-rich environments: gas-embedded star-forming regions (SFR), gas-enriched globular clusters, active galactic nucleus (AGN) discs, and protoplanetary discs. We find that gas-assisted binary capture is highly efficient in SFRs, potentially providing a main channel for the formation of binaries. It could also operate under certain conditions in gas-enriched globular clusters. Thin AGN discs could also provide a fertile ground for gas-assisted binary capture and in particular the formation of black hole/other compact object binaries, the production of gravitational-wave (GW) and other high-energy transients. Large-scale gaseous discs might be too thick to enable gas-assisted binary capture and previous estimates of the production of GW sources could be overestimated, and sensitive to specific conditions and the structure of the discs. In protoplanetary discs, while gas-assisted binary capture can produce binary Kuiper-belt objects, dynamical friction by small planetesimals is likely to be more efficient. Overall, we show that gas-assisted binary formation is robust and can contribute significantly to the binary formation rate in many environments. In fact, the gas-assisted binary capture rates are sufficiently high such that they will lead to multicaptures, and the formation of higher multiplicity systems.

Improved Quantum Molecular Dynamics Model and Its Application to Ternary Breakup Reactions

Collisions of very heavy nuclei 197Au+197Au at the energy range of 5–30 A MeV have been studied within the improved quantum molecular dynamics (ImQMD) model. A class of ternary events satisfying a nearly complete balance of mass numbers is selected and we find that the probability of ternary breakup depends on the incident energy and the impact parameter. It is also found that the largest probability of ternary breakup is located at the energy around 24 A MeV for the system 197Au+197Au. The experimental mass distributions and angular distributions for the system 197Au+197Au ternary breakup fragments can be reproduced well by the calculation with the ImQMD model at the energy of 15 A MeV. The modes and mechanisms of ternary and quaternary breakup are studied by time-dependent snapshots of ternary events. The direct prolate, direct oblate, and cascade ternary breakup modes, are manifested and their production probabilities are obtained. The characteristic features in ternary breakup events, three mass-comparable fragments, and the very fast, nearly collinear breakup, account for the two-preformed-neck shape of the composite system. The mean free path of nucleons in the reaction system is studied and the shorter mean free path is responsible for the ternary breakup with three mass comparable fragments, in which the two-body dissipation mechanism plays a dominant role.

Effective scattering and Efimov physics in the presence of two-body dissipation

Two-body dissipation usually gives rise to a complex interaction. Here we study the effect of two-body dissipation on few-body physics, including the fundamental two-body effective scattering and the three-body Efimov physics. By employing a two-channel model that incorporates the decay of closed-channel molecules (generating the two-body dissipation), we explicitly relate the real and imaginary part of the inverse scattering length (${a}_{s}^{\ensuremath{-}1}$) to closed-channel detuning and decay rate. In particular, we show that the imaginary part of ${a}_{s}^{\ensuremath{-}1}$ is given by the product of the molecule decay rate and the effective range. Such complex scattering length is found to generate an additional imaginary Coulomb potential when three atoms come close to each other, thereby suppressing the formation of trimer bound states and modifying the conventional discrete scaling in Efimov physics.

Complexity of Fermionic Dissipative Interactions and Applications to Quantum Computing

Interactions between particles are usually a resource for quantum computing, making quantum many-body systems intractable by any known classical algorithm. In contrast, noise is typically considered as being inimical to quantum many-body correlations, ultimately leading the system to a classically tractable state. This work shows that noise represented by two-body processes, such as pair loss, plays the same role as many-body interactions and makes otherwise classically simulable systems universal for quantum computing. We analyze such processes in detail and establish a complexity transition between simulable and nonsimulable systems as a function of a tuning parameter. We determine important classes of simulable and nonsimulable two-body dissipation. Finally, we show how using resonant dissipation in cold atoms can enhance the performance of two-qubit gates.

An average stochastic approach to two-body dissipation in finite fermion systems

We present average stochastic time-dependent Hartree–Fock (ASTDHF) as a theory for efficient handling of incoherent dynamical correlations in finite fermion systems at fully quantum-mechanical level. The basic time evolution is given by time-dependent mean-field theory. The two-body collisions beyond mean-field propagation are evaluated stochastically in an incoherent ensemble of mean-field states as was done in the previously developed STDHF. The new, and time saving, feature in ASTDHF is that it employs one common mean field throughout the whole ensemble. A detailed presentation of ASTDHF is given and extensive comparison with STDHF and other approaches to dissipation are discussed. ASTDHF is found to be a very efficient approach for well bound systems where mean-field fluctuations remain small.

Isoscalar giant monopole resonance within the Bohr-Mottelson model

Background: With the possibility to measure the isoscalar giant monopole resonance (ISGMR) in the short-lived nuclei, the compressibility of the open-shell and exotic nuclei has attracted much attention.Purpose: The present work is an attempt to develop a semiclassical model to describe the ISGMR and the compressibility of the finite nuclei.Method: The fluid dynamical reduction of the Boltzmann-Langevin equation was carried out to describe the collective motion of the nucleus [Z. Phys. A 337, 413 (1990); Z. Phys. A 349, 119 (1994)]. In this work, by including the Skyrme energy density functional, we develop the model and apply it to the ISGMR. Both the self-consistent and linearized methods are used to solve the corresponding Langevin equation.Results: It is shown that the calculations of the ISGMR energies in this work agree with those by the relativistic mean-field theory and the random phase approximation, and reproduce the general trend of the data. The model only includes the two-body dissipation, and underestimates the width of the ISGMR. Twelve sets of the Skyrme interactions are applied to perform the calculations and study the incompressibility parameters in the leptodermous expansion. The calculated surface parameter ${K}_{S}$ within the model is smaller than the extracted value, and decreases linearly over mass number of the nucleus. The calculated values of the symmetry parameter ${K}_{\ensuremath{\tau}}$ and the Coulomb parameter ${K}_{C}$ agree with the extracted values by fitting the available data for the nuclei from $^{12}\mathrm{C}$ to $^{238}\mathrm{U}$.Conclusions: The Bohr-Mottelson model provides a reasonable method to understand the ISGMR in a macroscopic approach.

Two-body dissipation effect in nuclear fusion reactions

Friction coefficients for the fusion reaction $^{16}$O+$^{16}$O $\rightarrow$ $^{32}$S are extracted based on both the time-dependent Hartree-Fock and the time-dependent density matrix methods. The latter goes beyond the mean-field approximation by taking into account the effect of two-body correlations, but in practical simulations of fusion reactions we find that the total energy is not conserved. We analyze this problem and propose a solution that allows for a clear quantification of dissipative effects in the dynamics. Compared to mean-field simulations, friction coefficients in the density-matrix approach are enhanced by about $20 \, \%$. An energy-dependence of the dissipative mechanism is also demonstrated, indicating that two-body collisions are more efficient at generating friction at low incident energies.

21aAC-7 重イオン核融合反応における2体散逸効果

21aAC-7 重イオン核融合反応における2体散逸効果

Two-body dissipation effects on the synthesis of superheavy elements

To investigate the two-body dissipation effects on the synthesis of superheavy elements, we calculate low-energy collisions of the $N=50$ isotones ($^{82}$Ge, $^{84}$Se, $^{86}$Kr and $^{88}$Sr) on $^{208}$Pb using the time-dependent density-matrix theory (TDDM). TDDM is an extension of the time-dependent Hartree-Fock (TDHF) theory and can determine the time evolution of one-body and two-body density matrices. Thus TDDM describes both one-body and two-body dissipation of collective energies. It is shown that the two-body dissipation may increase fusion cross sections and enhance the synthesis of superheavy elements.

Calculation of fission probability using one- and two-body dissipation in fusion-fission reactions

Calculation of fission probability using one- and two-body dissipation in fusion-fission reactions

ENHANCED ACCRETION RATES OF STARS ON SUPERMASSIVE BLACK HOLES BY STAR-DISK INTERACTIONS IN GALACTIC NUCLEI

We investigate the dynamical interaction of a central star cluster surrounding a super-massive black hole and a central accretion disk. The dissipative force acting on stars in the disk leads to an enhanced mass flow towards the super-massive black hole and to an asymmetry in the phase space distribution due to the rotating accretion disk. The accretion disk is considered as a stationary Keplerian rotating disk, which is vertically extended in order to employ a fully self-consistent treatment of stellar dynamics including the dissipative force originating from star-gas ram pressure effects. The stellar system is treated with a direct high-accuracy N-body integration code. A star-by-star representation, desirable in N-body simulations, cannot be extended to real particle numbers yet. Hence, we carefully discuss the scaling behavior of our model with regard to particle number and tidal accretion radius. The main idea is to find a family of models for which the ratio of two-body relaxation time and dissipation time (for kinetic energy of stellar orbits) is constant, which then allows us to extrapolate our results to real parameters of galactic nuclei. Our model is derived from basic physical principles and as such it provides insight into the role of physical processes in galactic nuclei, but it should be regarded as a first step towards more realistic and more comprehensive simulations. Nevertheless, the following conclusions appear to be robust: the star accretion rate onto the accretion disk and subsequently onto the super-massive black hole is enhanced by a significant factor compared to purely stellar dynamical systems neglecting the disk. This process leads to enhanced fueling of central disks in active galactic nuclei and to an enhanced rate of tidal stellar disruptions. [Abridged]

Nuclear dissipation effects on fission and evaporation in systems of intermediate fissility

The systems of intermediate fissility 132 Ce and 158 Er have been studied experimentally and theo- retically in order to investigate the dissipation properti es of nuclear matter. Cross sections of fusion-fission and evaporation residues channels together with charged particles multiplicities in both channels, their spectra, an- gular correlations and mass-energy distribution of fission fragments have been measured. Theoretical analysis has been performed using multi-dimensional stochastic approach with realistic treatment of particle evaporation. The results of analysis show that full one-body or unusually strong two-body dissipation allows to reproduce experimental data. No temperature dependent dissipation was needed.

Probing the Dissipation Mechanism in Ternary Reactions of 197Au+197Au by Mean Free Path of Nucleons

the collision of very heavy nuclei 197Au+197Au at 15 A MeV has been studied within the improved quantum molecular dynamics model. A class of ternary events satisfying nearly complete balance of mass numbers is selected. The experimental mass distributions for the system 197Au+197Au ternary fission fragments, the heaviest (A1), the intermediate (A2) and the lightest (A3), are reproduced well. The mean free path of nucleons in the reaction system is studied and the shorter mean free path is responsible for the ternary fission with three mass comparable fragments, in which the two-body dissipation mechanism plays a dominant role.

Understanding of the dissipation mechanism in ternary fission for the system 197Au+197Au

The mass number distributions of three fragments from the ternary fission of the system 197Au+197Au are reproduced rather well by using the improved quantum molecular dynamics (ImQMD) model without any adjusting parameter. It is found that the probability of ternary fission evidently depends on the incident energy and the impact parameter, and the two-body dissipation is the main mechanism responsible for the formation of the third fragment with comparable mass.

MACROSCOPIC DYNAMICAL DESCRIPTION OF ROTATING Au + Au SYSTEM

Events with more than two heavy fragments have been abundantly observed in heavy-ion semi-peripheral (fission-like) reaction 197 Au +197 Au at 15 MeV/nucleon. This raised interesting questions about their origin and about the time-scale at which they occur. As a possible explanation of this process, the surface instability of the cylindrical neck that is formed along the path from contact to reseparation of the rotating Au + Au system is investigated in the present paper. For this purpose the Los Alamos finite-range macroscopic dynamical model was used. The calculations were performed at relatively high angular momenta, L = 100 to 300 ħ, for two types of dissipation mechanisms: two-body viscosity and one-body dissipation. Various initial nuclear deformations and initial kinetic energies in the fission direction were considered. The resulting dynamical evolution in the multidimensional deformation space always led to multifragment scission configurations suggesting that ternary and quaternary break-up can occur during the heavy-ion reaction studied.

Fission rate in multi-dimensional Langevin calculations

Experimental data on nuclear dissipation have often been interpreted using one-dimensional model calculations of the Langevin or Fokker-Planck type. In the present work, the influence of the dimensionality of the deformation space on the time dependence of the fission process has been investigated in a systematic and quantitative way. In particular, the dependence of the transient time and the stationary value of the fission rate on the number of collective coordinates involved in Langevin calculations is investigated for the one-body and two-body dissipation mechanisms. We show that the results of Langevin-type calculations change appreciably if the deformation space is extended up to three dimensions.

DYNAMICAL EVOLUTION OF THE 197Au + 197Au SYSTEM AT 15 MeV/NUCLEON

Collisions of a very heavy 197 Au + 197 Au system have been studied at an energy of 15 MeV/nucleon with the aim to investigate a possible change of the energy dissipation mechanism from one-body dissipation (presumably dominating at low excitation energies) to two-body dissipation. The experiment was carried out in 4π geometry using the CHIMERA multidetector array. A class of ternary events satisfying nearly complete balance of mass numbers was selected. Preliminary results suggest that the selected ternary events represent mostly prompt ternary partitions of the colliding system, in which the lightest fragment is quite massive. In the light of theoretical predictions of Cârjan, Sierk and Nix this result may imply that the observed ternary reactions are driven by the two-body dissipation mechanism already at 15 MeV/nucleon.

The Dependency on the Dissipation Tensor of Multi-modal Nuclear Fission

In the study of the fission of actinide nuclei at low excitation energies including the spontaneous fission, it was found that the fragment mass distribution and the total kinetic energy (TKE) distribution consist of more than one component, in contrast to the simple single peak structure that is found in the fission at high excitation energies. 1– 6 This phenomenon is attributed to the existence of more than one fission path and is called the multi-modal fission. The mass and TKE distributions depend sensitively on the excitation energy and the position of the peaks of the mass distribution suggests the influence of the closed shell structure of the fragments. Therefore, it is supposed that the microscopic energy plays an important role for the manifestation of this phenomenon. It is a great challenge for us to understand this phenomenon in terms of nuclear many-body dynamics. Several authors studied the potential energy surface (PES) including the microscopic energy in a multi-dimensional parameter space that describes various nuclear shapes; one can deduce the possible fission paths by studying the location of the saddle points and the fission valleys in multi-dimensional parameter space. 7 With this method, they could explain the general trend of the position of the peaks of the mass distribution. The dynamical point of view is necessary to progress the study of the fission mode. We have applied the Langevin approach to the study of the fission modes in uranium nuclei and in fermium nuclei. 8–10 We studied the mass and TKE distributions and demonstrated that we can decompose the fission events into several components by tracing the Langevin trajectories. We also studied the isotope dependence and the excitation energy dependence of the fission mode. 8–10 In the previous studies, we adopted the wall-and-window type one-body friction as the dissipation mechanism of the nuclear fission dynamics. The validity of this dissipation mechanism has been demonstrated by one of the authors (T.W.) who studied the dissipation tensor dependence of the pre-scission neutron multiplicity and the mean TKE. 11–14 From the comparison of the results of the dynamical calculation with experimental data, they excluded the possibility of the two-body type dissipation to be the dominant mechanism by showing that it cannot reproduce the pre-scission neutron data and the TKE data simultaneously. On the other hand, they showed that the wall-and-window type one-body friction can reproduce both data reasonably well and concluded that it is a reasonable model for the dissipation mechanism of nuclear fission. There are other models that are of one-body nature, e.g. surface-plus-window formula, modified wall-and-window formula and chaos weighted wall formula. 15–17 Though there were no free parameters in the original derivation of the one-body friction, 18, 19 the strength has been modified frequently in order to reproduce some experimental data. For example, in the study of the light particle evaporation and the mass distribution, Schmitt et al. used the strength as a free parameter. 17 The modification itself should be acceptable when we take account of the simplicity of the model; it is a macroscopic model without any microscopic effect and it has no dependence on the temperature. However, when one modifies the strength of the nuclear dissipation just to reproduce only one physical quantity, it might be inappropriate to conclude that the deduced strength has definite physical meanings. It may reflect the other effects completely different from the dissipation, like the insufficiency of the model space. It is very important to compare many (at least more than one) physical quantities at the same time. Among the physical quantities that are measured in nuclear fission, the TKE and mass distributions are well investigated experimentally in many cases. In this study, we use these quantities to discuss the dissipation dependence of the fission modes. It is shown that the TKE distribution is, as was expected, directly connected to the strength of the dissipation and we can put some constraints on the strength of the dissipation. Furthermore, it is shown that the mass distribution changes rather drastically when one uses different models for the dissipation mechanism. These results demonstrate the importance and the usefulness of the dynamical approach to the study of the fission mode. Section 2 gives a concise description of our framework. Results are shown in Sec. 3 concerning the fission of 264 Fm nucleus at Ex = 20 MeV. Summary is given in Sec. 4. 2. Methods