arXiv subjects

Ryusuke Hamazaki

Publications and source records attributed to Ryusuke Hamazaki.

At least 37 records · Page 2Linked to original sources

arXiv2025

Measurement-Induced Spectral Transition

We show that noisy quantum dynamics exposed to weak measurements exhibit a spectral transition between gapless and gapped phases. To this end, we employ the Lyapunov spectrum obtained through singular values of a non-unitary matrix describing the dynamics. We discover that the gapless and gapped phases respectively correspond to the volume-law and area-law phases of the entanglement entropy for the dominant Lyapunov vector. This correspondence between the spectral gap and the scaling of entanglement offers an intriguing analogy with ground-state phase transitions. We also discuss some crucial differences from ground-state transitions, such as the scaling law of the entanglement and the exponentially small gaps. Furthermore, we show that the spectral transition leads to the transition of the timescale for the memory loss of initial states.

quant-ph↗

arXiv2024

Speed limits to fluctuation dynamics

Fluctuation dynamics of an experimentally measured observable offer a primary signal for nonequilibrium systems, along with dynamics of the mean. While universal speed limits for the mean have actively been studied recently, constraints for the speed of the fluctuation have been elusive. Here, we develop a theory concerning rigorous limits to the rate of fluctuation growth. We find a principle that the speed of an observable's fluctuation is upper bounded by the fluctuation of an appropriate observable describing velocity, which also indicates a tradeoff relation between the changes for the mean and fluctuation. We demonstrate the advantages of our inequalities for processes with non-negligible dispersion of observables, quantum work extraction, and the entanglement growth in free fermionic systems. Our results open an avenue toward a quantitative theory of fluctuation dynamics in various non-equilibrium systems encompassing quantum many-body systems and nonlinear population dynamics.

cond-mat.stat-mech↗

arXiv2024

Kinetically constrained models constructed from dissipative quantum dynamics

We propose a construction of kinetically constrained models using the Markovian quantum dynamics under strong dissipation. Engineering the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation through classical noise, we show that strong dissipation leads to the emergent decoherence-free subspaces, within which constrained quantum many-body unitary dynamics can take place. We argue that the unitary dynamics constructed by the GKSL dynamics is more tightly constrained than that constructed by the strongly interacting Hamiltonian, where the interactions have the same form with the GKSL jump operators. As an example, we demonstrate that a one-dimensional spin system with two-site dissipation leads to the kinetically constrained "PXQ" model, which exhibits the free domain-wall motion with an additional frozen-block structure. Under a uniform magnetic field, the PXQ model shows the domain-wall localization, similar to the Wannier-Stark localization. We then couple two PXQ chains with the magnetic field by an inter-chain interaction. We discover that, while localization of the domain walls persists despite the interactions for typical parameter regimes, a non-trivial partial delocalization appears for a certain parameter line.

quant-ph↗

arXiv2024

Quantum Velocity Limits for Multiple Observables: Conservation Laws, Correlations, and Macroscopic Systems

How multiple observables mutually influence their dynamics has been a crucial issue in statistical mechanics. We introduce a new concept, "quantum velocity limits," to establish a quantitative and rigorous theory for non-equilibrium quantum dynamics for multiple observables. Quantum velocity limits are universal inequalities for a vector the describes velocities of multiple observables. They elucidate that the speed of an observable of our interest can be tighter bounded when we have knowledge of other observables, such as experimentally accessible ones or conserved quantities, compared with the conventional speed limits for a single observable. We first derive an information-theoretical velocity limit in terms of the generalized correlation matrix of the observables and the quantum Fisher information. The velocity limit has various novel consequences: (i) conservation law in the system, a fundamental ingredient of quantum dynamics, can improve the velocity limits through the correlation between the observables and conserved quantities; (ii) speed of an observable can be bounded by a nontrivial lower bound from the information on another observable; (iii) there exists a notable non-equilibrium tradeoff relation, stating that speeds of uncorrelated observables, e.g., anti-commuting observables, cannot be simultaneously large; (iv) velocity limits for any observables on a local subsystem in locally interacting many-body systems remain convergent even in the thermodynamic limit. Moreover, we discover another distinct velocity limit for multiple observables on the basis of the local conservation law of probability current, which becomes advantageous for macroscopic transitions of multiple quantities.

cond-mat.stat-mech↗

arXiv2024

Absorption to Fluctuating Bunching States in Non-Unitary Boson Dynamics

We show that noisy nonunitary dynamics of bosons drives arbitrary initial states into a novel fluctuating bunching state, where all bosons occupy one time-dependent mode. We propose a concept of the noisy spectral gap, a generalization of the spectral gap in noiseless systems, and demonstrate that the exponentially fast absorption to the fluctuating bunching state takes place asymptotically. The fluctuating bunching state is unique to noisy nonunitary dynamics, with no counterpart in any unitary dynamics and nonunitary dynamics described by a time-independent generator. We also argue that the times of relaxation to the fluctuating bunching state obey a universal power law as functions of the noise parameter in generic noisy nonunitary dynamics.

quant-ph↗

arXiv2023

Role of Topology in Relaxation of One-Dimensional Stochastic Processes

Stochastic processes are commonly used models to describe dynamics of a wide variety of nonequilibrium phenomena ranging from electrical transport to biological motion. The transition matrix describing a stochastic process can be regarded as a non-Hermitian Hamiltonian. Unlike general non-Hermitian systems, the conservation of probability imposes additional constraints on the transition matrix, which can induce unique topological phenomena. Here, we reveal the role of topology in relaxation phenomena of classical stochastic processes. Specifically, we define a winding number that is related to topology of stochastic processes and show that it predicts the existence of a spectral gap that characterizes the relaxation time. Then, we numerically confirm that the winding number corresponds to the system-size dependence of the relaxation time and the characteristic transient behavior. One can experimentally realize such topological phenomena in magnetotactic bacteria and cell adhesions.

cond-mat.stat-mech↗

arXiv2023

Quasiparticles of Decoherence Processes in Open Quantum Many-Body Systems: Incoherentons

The relaxation dynamics of an open quantum system is determined by the competition between the coherent Hamiltonian dynamics of a system and the dissipative dynamics due to interactions with environments. It is therefore of fundamental interest to understand the transition from the coherent to incoherent regimes. We find that hitherto unrecognized quasiparticles -- incoherentons -- describe this coherent-to-incoherent transition in eigenmodes of a Liouvillian superoperator that governs the dynamics of an open quantum many-body system. Here, an incoherenton is defined as an interchain bound state in an auxiliary ladder system that represents the density matrix of a system. The Liouvillian eigenmodes are classified into groups with different decay rates that reflect the number of incoherentons involved therein. We also introduce a spectral gap -- quantum coherence gap -- that separates the different groups of eigenmodes. We demonstrate the existence of incoherentons in a lattice boson model subject to dephasing, and show that the quantum coherence gap closes when incoherentons are deconfined, which signals a dynamical transition from incoherent relaxation with exponential decay to coherent oscillatory relaxation. Furthermore, we discuss how the decoherence dynamics of quantum many-body systems can be understood in terms of the generation, localization, and diffusion of incoherentons.

quant-ph↗

arXiv2023

Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry

We elucidate how the presence of higher-form symmetries affects the dynamics of thermalization in isolated quantum systems. Under reasonable assumptions, we analytically show that a $p$-form symmetry in a $(d+1)$-dimensional quantum field theory leads to the breakdown of the eigenstate thermalization hypothesis for many nontrivial $(d-p)$-dimensional observables. For higher-form (i.e., $p\geq 1$) symmetry, this indicates the absence of thermalization for observables that are non-local but much smaller than the whole system size. We numerically demonstrate this argument for the (2+1)-dimensional $\mathbb{Z}_2$ lattice gauge theory. While local observables such as the plaquette operator thermalize, the non-local observable exciting a magnetic dipole instead relaxes to the generalized Gibbs ensemble that takes account of the $\mathbb{Z}_2$ 1-form symmetry.

cond-mat.stat-mech↗

arXiv2023

Localization properties in disordered quantum many-body dynamics under continuous measurement

We study localization properties of continuously monitored dynamics and associated measurement-induced phase transitions in disordered quantum many-body systems on the basis of the quantum trajectory approach. By calculating the fidelity between random quantum trajectories, we demonstrate that the disorder and the measurement can lead to dynamical properties distinct from each other, although both have a power to suppress the entanglement spreading. In particular, in the large-disorder regime with weak measurement, we elucidate that the fidelity exhibits an anomalous power-law decay before saturating to the steady-state value. Furthermore, we propose a general method to access physical quantities for quantum trajectories in continuously monitored dynamics without resorting to postselection. It is demonstrated that this scheme drastically reduces the cost of experiments. Our results can be tested in ultracold atoms subject to continuous measurement and open the avenue to study dynamical properties of localization, which cannot be understood from the stationary properties of the entanglement entropy.

cond-mat.stat-mech↗

arXiv2023

Distinguishability Transitions in Non-Unitary Boson Sampling Dynamics

We discover novel transitions characterized by distinguishability of bosons in non-unitary dynamics with parity-time ($\mathcal{PT}$) symmetry. We show that $\mathcal{PT}$ symmetry breaking, a unique transition in non-Hermitian open systems, enhances regions in which bosons can be regarded as distinguishable. This means that classical computers can sample the boson distributions efficiently in these regions by sampling the distribution of distinguishable particles. In a $\mathcal{PT}$-symmetric phase, we find one dynamical transition upon which the distribution of bosons deviates from that of distinguishable particles, when bosons are initially put at distant sites. If the system enters a $\mathcal{PT}$-broken phase, the threshold time for the transition is suddenly prolonged, since dynamics of each boson is diffusive (ballistic) in the $\mathcal{PT}$-broken ($\mathcal{PT}$-symmetric) phase. Furthermore, the $\mathcal{PT}$-broken phase also exhibits a notable dynamical transition on a longer time scale, at which the bosons again become distinguishable. This transition, and hence the classical easiness of sampling bosons in long times, are true for generic postselected non-unitary quantum dynamics, while it is absent in unitary dynamics of isolated quantum systems. $\mathcal{PT}$ symmetry breaking can also be characterized by the efficiency of a classical algorithm based on the rank of matrices, which can (cannot) efficiently compute the photon distribution in the long-time regime of the $\mathcal{PT}$-broken ($\mathcal{PT}$-symmetric) phase.

quant-ph↗

arXiv2022

Quantum Metrology Protected by Hilbert Space Fragmentation

We propose an entanglement-enhanced sensing scheme that is robust against spatially inhomogeneous always-on Ising interactions. Our strategy is to tailor coherent quantum dynamics employing the Hilbert-space fragmentation (HSF), a recently recognized mechanism that evades thermalization in kinetically constrained many-body systems. Specifically, we analytically show that the emergent HSF caused by strong Ising interactions enables us to design a stable state where part of the spins is effectively decoupled from the rest of the system. Using the decoupled spins as a probe to measure a transverse field, we demonstrate that the Heisenberg limited sensitivity is achieved without suffering from thermalization.

quant-ph↗

arXiv2022

Emergence of Hilbert Space Fragmentation in Ising Models with a Weak Transverse Field

The transverse-field Ising model is one of the fundamental models in quantum many-body systems, yet a full understanding of its dynamics remains elusive in higher than one dimension. Here, we show for the first time the breakdown of ergodicity in $d$-dimensional Ising models with a weak transverse field in a prethermal regime. We demonstrate that novel Hilbert-space fragmentation occurs in the effective non-integrable model with $d\geq2$ as a consequence of only one emergent global conservation law of the domain wall number. Our results indicate nontrivial initial-state dependence for non-equilibrium dynamics of the Ising models in a weak transverse field.

cond-mat.stat-mech↗

arXiv2022

Bounds in Nonequilibrium Quantum Dynamics

We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical stochastic systems. We start from the speed limits, the universal bounds on the speeds of (either quantum or classical) dynamical evolutions. We then turn to review the bounds that address how good and how long would a quantum system equilibrate or thermalize. Afterward, we focus on the stringent constraint set by locality in many-body systems, rigorously formalized as the Lieb-Robinson bound. We also review the bounds related to the dynamics of entanglement, a genuine quantum property. Apart from some other miscellaneous topics, several notable error bounds for approximated quantum dynamics are discussed. While far from comprehensive, this topical review covers a considerable amount of recent progress and thus could hopefully serve as a convenient starting point and up-to-date guidance for interested readers.

quant-ph↗

arXiv2022

Lindbladian Many-Body Localization

We discover a novel localization transition that alters the dynamics of coherence in disordered many-body spin systems subject to Markovian dissipation. The transition occurs in the middle spectrum of the Lindbladian super-operator whose eigenstates obey the universality of non-Hermitian random-matrix theory for weak disorder and exhibit localization of off-diagonal degrees of freedom for strong disorder. This Lindbladian many-body localization prevents many-body decoherence due to interactions and is conducive to robustness of the coherent dynamics characterized by the rigidity of the decay rate of coherence.

cond-mat.dis-nn↗

arXiv2022

Eigenstate Thermalization in Long-Range Interacting Systems

Motivated by recent ion experiments on tunable long-range interacting quantum systems [B.Neyenhuis et al., Sci.Adv.3, e1700672 (2017, https://doi.org/10.1126/sciadv.1700672 )], we test the strong eigenstate thermalization hypothesis (ETH) for systems with power-law interactions $\sim 1/r^α$. We numerically demonstrate that the strong ETH typically holds at least for systems with $α\geq 0.6$, which include Coulomb, monopole-dipole, and dipole-dipole interactions. Compared with short-range interacting systems, the eigenstate expectation value of a generic local observable is shown to deviate significantly from its microcanonical ensemble average for long-range interacting systems. We find that Srednicki's ansatz breaks down for $α\lesssim 1.0$ at least for relatively large system sizes.

cond-mat.stat-mech↗

arXiv2022

Speed Limits for Macroscopic Transitions

Speed of state transitions in macroscopic systems is a crucial concept for foundations of nonequilibrium statistical mechanics as well as various applications in quantum technology represented by optimal quantum control. While extensive studies have made efforts to obtain rigorous constraints on dynamical processes since Mandelstam and Tamm, speed limits that provide tight bounds for macroscopic transitions have remained elusive. Here, by employing the local conservation law of probability, the fundamental principle in physics, we develop a general framework for deriving qualitatively tighter speed limits for macroscopic systems than many conventional ones. We show for the first time that the speed of the expectation value of an observable defined on an arbitrary graph, which can describe general many-body systems, is bounded by the "gradient" of the observable, in contrast with conventional speed limits depending on the entire range of the observable. This framework enables us to derive novel quantum speed limits for macroscopic unitary dynamics. Unlike previous bounds, the speed limit decreases when the expectation value of the transition Hamiltonian increases; this intuitively describes a new tradeoff relation between time and quantum phase difference. Our bound is dependent on instantaneous quantum states and thus can achieve the equality condition, which is conceptually distinct from the Lieb-Robinson bound. Our work elucidates novel speed limits on the basis of local conservation law, providing fundamental limits to various types of nonequilibrium quantum macroscopic phenomena.

cond-mat.stat-mech↗

arXiv2022

Impact of Dissipation on Universal Fluctuation Dynamics in Open Quantum Systems

Recent experimental and theoretical works have uncovered nontrivial quantum dynamics due to external dissipation. Using an exact numerical method and a renormalization-group-based analytical technique, we theoretically elucidate that dissipation drastically alters universal particle-number-fluctuation dynamics related to surface-roughness growth in non-interacting fermions and bosons. In a system under dephasing that causes loss of spatial coherence, we find that a universality class of surface-roughness dynamics changes from the ballistic class to a class with the Edwards-Wilkinson scaling exponents and an unconventional scaling function. On the other hand, in a system under dissipation with in- and out-flow of particles that breaks particle-number conservation, the universal dynamics is lost.

quant-ph↗

arXiv2022

Universal constraint on nonlinear population dynamics

Ecological and evolutionary processes show various population dynamics depending on internal interactions and environmental changes. While crucial in predicting biological processes, discovering general relations for such nonlinear dynamics has remained a challenge. Here, we derive a universal information-theoretical constraint on a broad class of nonlinear dynamical systems represented as population dynamics. The constraint is interpreted as a generalization of Fisher's fundamental theorem of natural selection. Furthermore, the constraint indicates nontrivial bounds for the speed of critical relaxation around bifurcation points, which we argue are universally determined only by the type of bifurcation. Our theory is verified for an evolutionary model and an epidemiological model, which exhibit the transcritical bifurcation, as well as for an ecological model, which undergoes limit-cycle oscillation. This work paves a way to predict biological dynamics in light of information theory, by providing fundamental relations in nonequilibrium statistical mechanics of nonlinear systems.

physics.bio-ph↗