Top PDF Disorder Driven Transitions in Non-Equilibrium Quantum Systems

Disorder Driven Transitions in Non-Equilibrium Quantum Systems

Disorder Driven Transitions in Non-Equilibrium Quantum Systems

The above properties describe the single particle characteristics of the AFAI, and lead to its defining characteristic as a many body system: robust quantized charge pumping that persists in a non-adiabatic driving regime. This behavior is in con- trast to that of the one-dimensional “Thouless pump,” where the pumped charge is quantized only in the limit of infinitely slow driving [105]. The setup that realizes non-adiabatic quantized pumping is illustrated in Fig. 8.1. We consider a strip of AFAI in which all of the states close to one edge are populated with fermions. In this situation, the total current flowing through the strip is quantized as an integer times the inverse driving period, hIi = eW /T . Here, W is the bulk winding number char- acterizing the parent anomalous Floquet topological phase. The current averaged over many driving periods is hIi. The quantized charge pumping is a direct result of the edge structure defined above: when the fermion occupation is of the form shown in Fig. 8.1, the edge states on one side are completely filled, while the localization of the bulk states prevents current from flowing in the direction perpendicular to the edge. In Sec. 8.4, we derive the relation between the quantization of the charge current and the bulk topological invariant, and discuss temporal fluctuations about the quantized value.
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Absence of Disorder-Driven Metal-Insulator Transitions in Simple Holographic Models

Absence of Disorder-Driven Metal-Insulator Transitions in Simple Holographic Models

strongly interacting many-body quantum systems. In many of these systems, macroscopic observables are gov- erned by quantum critical physics. One such observable is the electrical conductance at finite temperature, den- sity and disorder. Unfortunately, there are few reliable theoretical methods for such strongly coupled regimes. Some recent work has advocated the memory matrix for- malism [6–9], in combination with hydrodynamic insight [10]. These methods may be used directly in microscopic models [11–13]. However, this approach is perturbative in disorder, and may not be adequate for understanding non-Drude physics in strange metals [14].
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Nonequilibrium effective field theory for absorbing state phase transitions in driven open quantum spin systems

Nonequilibrium effective field theory for absorbing state phase transitions in driven open quantum spin systems

The directed percolation class is conjectured [29,30] to en- compass all systems featuring a one-component order param- eter, short-range interactions, no additional symmetries, and a unique, fluctuationless absorbing state. This last condition is crucial; the difficulty in having a perfectly fluctuation-free state in real systems has made it a challenge to identify experimental setups undergoing a phase transition in this class [31]. The first clear examples have only recently been highlighted in two-dimensional nematic liquid crystals [32,33] and one- [34] and two-dimensional [35] turbulent flows. In addition, a recent numerical study links DP to the onset of turbulence in quantum fluids (such as superfluids) [36]. Upon relaxing the other assumptions, different transitions, alongside their universality classes, have been identified and investigated: for instance, the introduction of quenched spatial randomness [37–39] makes the DP critical point unstable (it constitutes a “relevant” perturbation in the renormalization group sense) and generates nonuniversal power laws; the presence of multiple absorbing states often leads to the appearance of discontinuous transitions [40,41]; other symmetries, such as preservation of the parity of active sites [42,43], also change the critical properties, as does introducing long-range processes (L´evy flights) [44]. As in equilibrium systems, multicritical behavior can emerge when higher-order processes take over the simple ones in Eq. (1.1) [45,46]. A simple example studied in the literature is the so- called tricritical directed percolation [30,47,48], obtained, e.g., by adding processes involving pairs such as ↑↑↓ → ↑↑↑ or ↑↑ → ↓↓. Depending on the relative rates of these processes compared to the ordinary DP ones, the transition may become first order by crossing a bicritical point. 1
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Strongly correlated quantum fluids and effective thermalization in non-Markovian driven-dissipative photonic systems

Strongly correlated quantum fluids and effective thermalization in non-Markovian driven-dissipative photonic systems

This chapter is organized as follow: we introduce in Sec. 2.2 a quantum optics scheme in an array of driven-dissipative nonlinear resonators with embedded incoherently pumped two-level emitters. Projective methods are used to eliminate the emitter dynamics and write a generalized master equation for the photonic degrees of freedom only, where the frequency- dependence of gain introduces non-Markovian features. As a rst step, in Sec. 2.3, we look at the various steady-state features in a single cavity conguration: for weak nonlinearities, this pumping scheme provides exotic optical bistability eects, not induced by the presence of a coherent incident pump, but rather by the frequency dependence of the non-Markovian gain medium. In the blockade regime, this scheme allows for the selective generation of Fock states with a well-dened photon number, which is an essential step toward the stabilization of strongly correlated many-body phases with photons. We then move to the investigation of the phenomenology in the many-cavity conguration: in Sec. 2.4 we analyse some general properties and show that the steady-state presents thermal properties when the emission spectrum is broad with respect to Hamiltonian frequency-scales. In Sec. 2.5 we briey discuss an exotic mechanism leading to the emergence of coherence in presence of nite interactions. In Sec. 2.6 we analyse the steady-state properties in the strong blockade regime: rst, we conrm the existence of a Mott phase for weak inter-cavity hopping. We show however that this state is not fully robust, as for a hopping constant exceeding the spectral emission linewidth, the commensurability condition on density is not sustainable anymore and holes are generated with the system, and analyse the one-body correlations close to the Mott regime. Finally, in Sec. 2.7, we investigate the Gutzwiller Mean-Field phase diagram of such a system. and unveil a Mott-to-Superuid phase transition triggered by the same proliferation of hole excitations involved in the depletion of the MI state. We nd that, at a critical value of the inter-cavity photon hopping, the system undergoes a second-order nonequilibrium phase phase transition (of a Mott-to-Superuid type) associated with the spontaneous breaking of the U (1) symmetry. Unlike the equilibrium case, the transition is always driven by commensurability eects for this model, and not by the competition between photon hopping and optical nonlinearity. The corresponding phase boundary is characterized numerically, and also accessed also analytically in the specic case of the Hard-Core regime.
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Absence of disorder-driven metal-insulator transitions in simple holographic models.

Absence of disorder-driven metal-insulator transitions in simple holographic models.

The advent of gauge-gravity duality [15 – 17] has allowed for controlled, nonperturbative transport computations in a strongly interacting quantum system. The quantum dynam- ics is holographically encoded in the classical response of a black hole in an asymptotically anti – de Sitter (AdS) spacetime in one higher dimension. These systems have large N matrix degrees of freedom, but we focus on correlators of charge currents in this Letter. Correlation functions of simple macroscopic observables are controlled by symmetries and often do not sensitively depend on the underlying large N matrix model. Early efforts to compute transport coefficients entirely from holography were sty- mied by a simple theorem: A Galilean-invariant, charged fluid has zero electrical resistance (currents are obtained at no energy cost by changing the reference frame). Recently, numerical approaches to general relativity advanced to the point where the transport problem can be solved in numerically constructed black hole backgrounds which break translational symmetry [18 – 26], giving finite elec- trical conductivity σ at finite density. Perturbative analytic
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Thermalization in Periodically-Driven Interacting Quantum Systems

Thermalization in Periodically-Driven Interacting Quantum Systems

appropriately such that the nonequilibrium steady state (NESS) of system is controlled. This is the subject of chapters 2 and 3 and Refs. [14, 31, 32, 76].Second, one can still isolate the system but hope to find parameter regimes in which the heating process is slow compared to any desired physics of interest. This is called prethermalization, or rather finding regimes where there are long-lived transient states [2, 9, 21, 44, 52, 88, 91]. A “dual” version of prethermalization is to look for stationary states of finite systems that do not exhibit maximal entropy (heating). This is the subject of chapter 4. Third, one can study integrable, or more generally “non-ergodic," Floquet models where an extensive (in system size) number of local conserved quantities restrict mixing in the Hilbert space thereby forbidding heating - this is not a generic situation, especially in an experiment, but it serves as a good starting point for studying heating in closed systems [25, 78, 89].An example of this non-ergodic behavior is the extension of many-body localization (MBL) to the Floquet setting [1, 3, 18, 39, 48, 61, 62]. Bordia et al. [7] have periodically driven a system of cold atoms in a disordered optical lattice and demonstrated the existence of non- thermal phase. Finally, one can consider off-resonant Floquet systems in which drives are used to perturbatively modify the system but do not directly allow energetic transitions in the system. This approach has been studied using high frequency expansions as in Refs. [8, 26].
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Disordered driven coupled cavity arrays : Non equilibrium stochastic mean field theory

Disordered driven coupled cavity arrays : Non equilibrium stochastic mean field theory

Let us note at this stage that although the existence of bistability is due to the mean-field decoupling, its presence is indicative of physically meaningful bimodal distributions in the true density matrix [36,37]. The equation of motion for the full-system density matrix is linear and so either has a unique steady state or a degenerate subspace of steady states. The mean-field decoupling instead produces a nonlinear equation for the single-site density matrix, which may have multiple distinct solutions—these distinct solutions can thus describe bistability. Where mean-field theory would predict bistability, the full density matrix would generally have a configuration with a significant weight near both of these mean-field solutions, but with a fixed ratio between their weights and a tail of finite probability states that connect these. Both the ratio of weights and the existence of the intermediate states cannot be found by mean-field theories and require consideration of fluctuations, specifically instanton and soliton corrections that would describe tunneling between different mean-field configurations [38]. It is, however, worth noting that all these statements relate to the ensemble av- eraged steady state of the system. If a system is prepared near to one of the two bistable states, the subsequent dynamics will initially remain near that configuration until a tunneling event causes a transition to the other state. Such tunneling (quantum, thermal, or induced by external noise) can cause transitions in both directions and eventually produces a fixed ratio between the two parts of the bimodal distribution.
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Quantum order by disorder driven phase reconstruction in the vicinity of ferromagnetic quantum critical points

Quantum order by disorder driven phase reconstruction in the vicinity of ferromagnetic quantum critical points

We have used this approach to investigate fluctuation-driven phase reconstruction in the vicinity of an itinerant ferromag- netic quantum critical point in three spatial dimensions. This quantum critical point is unstable toward the formation of spiral and spin-nematic states. Quantum fluctuations would render the transition between the uniform ferromagnet and the paramagnet first order. However, this first-order transition is preempted by a modulated spiral ferromagnetic phase. At even lower temperatures, a d -wave spin-nematic state forms, which is slightly favored over a spin nematic with p-wave symmetry. It is located between the paramagnetic and the spiral phases. In order to describe more generic experimental systems, we determined the phase diagram in the presence of an anisotropic electron dispersion. The regions of phase space occupied by both the spiral and the spin-nematic phases are enlarged. Moreover, the onset of spiral order is no longer coincident with the putative tricritical point of the uniform ferromagnet, and the order of transitions is modified.
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Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices

Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices

An important tool available in ultracold atomic setups is provided by the control of the dimensionality and the geometry of superimposed optical lattices. Such a control has been recently used in an experimental implementa- tion of honeycomb lattices for ultracold fermions [6]. Sev- eral schemes have been discussed in the literature [7, 8] with the aim of engineering topologically non-trivial two- dimensional systems on honeycomb lattices, which nat- urally reproduce well-known paradigmatic models such as the Haldane model [9]. The discussed setups rely on the laser implementation of tight-binding models on hon- eycombs having both nearest-neighbor and next-nearest- neighbor hoppings: these hoppings simulate the presence of a staggered magnetic field which breaks time-reversal symmetry and opens band gaps. In this way one can ob- tain different topological phases, usually corresponding to topological insulators or semimetals, which mimic the quantum Hall physics and present different patterns of protected edge states.
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Driven dissipative dynamics and topology of quantum impurity systems

Driven dissipative dynamics and topology of quantum impurity systems

Fig. 2. (a) Evolution of the Rabi dynamics P ( t ) = σ z ( t ) as a function of the coupling with the environment with the first implementation of the stochastic Schrödinger equation approach with one stochastic field (see Eq. (17)). (b) Quality factor / γ of the damped oscillations and comparison with Eq. (15) derived within the NIBA approximation. In Refs. [70,71], there is a precise comparison between the effects of increasing the coupling with the environment at T = 0 and of increasing the temperature. Recent developments with more than one stochastic fields allow us to approach the point α = 1 / 2 more closely [74]. However, the method still suffers for α > 1 / 2 from convergence problems. For two spins, the quantum phase transition occurs for smaller coupling strengths allowing a very precise analysis of the dynamics in the localized phase [73]. (c) Cartoon of spin winding on the Bloch sphere in relation with the d-vector d = ( H sin θ d cos φ d , H sin θ d sin φ d , H cos θ d ) when θ d vary. Note that it is sufficient to consider the variation of the ground state with θ d to characterize the topology due to azimuthal symmetry of the spin–boson Hamiltonian. (d) Result obtained from the Stochastic Schrödinger Equation showing that the “non-adiabatic” Chern number C dyn can become non-quantized and be strongly reduced (compared to the equilibrium quantized Chern number C = 1) when increasing the dissipation strength; here v / H = 0 . 08 and H / ω c = 0 . 01 [74]. The crossover occurs when r ∼ v since C = C dyn + O ( v / r ) . (inset) We show the effective temperature T eff (defined as T ∗ for this particular protocol). There is an inversion of population when C dyn = 1 / 2 and the environment produces an effective field compensating for the applied field. In Sec. 2.7, we describe a simple toy mean-field model to describe this quantum dynamo effect, which occurs for half a Floquet time period, and therefore on short time scales.
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Non equilibrium processes and ergodicity breaking in isolated quantum systems

Non equilibrium processes and ergodicity breaking in isolated quantum systems

transition). The transport is subdiffusive for all disorder strengths in the strongly interacting regime (∆ > 1), while a transition between diffusive and subdiffusive transport exists at finite W in weakly interacting systems (∆ < 1) [62]. This anomalous transport has been linked to long-tailed (i.e. non-Gaussian) distributions for the off-diagonal matrix elements of local spin operators in the ergodic phase [63]. It was found that these systems satisfy a modified version of the ETH in the subdiffusive regime, in which the scaling of the variance of the off-diagonal matrix elements with system size requires power-law corrections to the exponential in (1.14) [63]. Furthermore, it has been shown that energy transport is diffusive when the disorder is weak, and the system undergoes a transition to subdiffusive transport at a finite disorder strength (which depends on the strength of the interactions) before the MBL transition [64–66]. Subdiffusive spin transport has also been observed in a periodically driven Floquet version of the model, with associated long-tailed distributions of the matrix elements of local spin operators in the eigenstates of the Floquet unitary [67]. It is interesting to note that in this system, which does not conserve energy, the MBL phase is still present [68–72].
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Non equilibrium quantum dynamics : interplay of disorder, interactions and confinement

Non equilibrium quantum dynamics : interplay of disorder, interactions and confinement

3.2 integrability and the generalised gibbs ensemble In classical physics the notion of integrability is well defined. An in- tegrable system with n degrees of freedom will possess n independ- ent first integrals of motion that are Poisson-commuting and can thus be called ‘integrable’. The terminology follows from the fact that it is then possible to integrate the resulting differential equations describ- ing the time evolution and the solutions will display periodic motion on tori in phase space where ergodicity is absent. This clear definition is not possible in quantum mechanics where already the definition of degrees of freedom is very different. In fact it was shown by Caux and Mossel [36] that we currently do not possess a commonly accep- ted and self-consistent definition of quantum integrability. It is how- ever possible to define integrability in a practical sense. We therefore call a quantum system integrable if it is Bethe Ansatz solvable [61] or non-interacting (its Hamiltonian is quadratic in the fermionic (bo- sonic) creation and annihilation operators). Strictly speaking, the lat- ter already entails the former. Usually integrable systems constitute isolated points in parameter space meaning that when we add weak perturbations, they become generic. They further contain a large num- ber (extensively many) of conserved quantities. Lastly we note that in- tegrability in quantum systems is linked to Poisson level statistics [36], something we discuss further in Sec. 3.4.2.
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Interplay of Quantum Stochastic and Dynamical Maps to Discern Markovian and Non Markovian Transitions

Interplay of Quantum Stochastic and Dynamical Maps to Discern Markovian and Non Markovian Transitions

The contents are organized as follows: In Section 2 some basic concepts [7,8] on A and B maps are given. The emergence of CP/NCP maps, at intermediate times, under open system dynamics is discussed in Section 3. Section 4 is devoted to a powerful link (brought out by Jamiolkowski isomorphism) between the B map and the dynamical state. Some illustrative examples of dynamical B map to investigate the CP/NCP nature of dynamics at intermediate times are discussed in Section 5. The exam- ples are chosen from different origins: one based entirely from the general considerations of Jamiolkowski iso- morphism; second one on the recent all-optical open sys- tem experiment to drive Markovian to non-Markovian transitions; the other two examples are based on open system Hamiltonian dynamics. In all these four examples, no master equation is employed in the deduction of Markov to non-Markov transitions—but the CP/NCP nature of the intermediate dynamical map (via the sign of the eigenvalue of the B map) has been invoked. Section 6 has some concluding remarks.
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Avoided crossing and sub-Fourier-sensitivity in driven quantum systems

Avoided crossing and sub-Fourier-sensitivity in driven quantum systems

(Received 27 June 2018; revised manuscript received 28 September 2018; published 21 November 2018) The response of a linear system to an external perturbation is governed by the Fourier limit, with the inverse of the interaction time constituting a lower limit for the system bandwidth. This does not hold for nonlinear systems, which can thus exhibit sub-Fourier-behavior. The present Letter identifies a mechanism for sub-Fourier-sensitivity in driven quantum systems, which relies on avoided crossing between Floquet states. Features up to three orders of magnitude finer than the Fourier limit are presented.
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Large scale dynamics and fluctuations in non equilibrium stochastic particle systems

Large scale dynamics and fluctuations in non equilibrium stochastic particle systems

In Chapter 5, we study lower current large deviations for general TAZRP with concave flux functions J (ρ), which can be realized by phase separated density profiles. Travelling wave profiles related to non-entropic hydrodynamic shocks are identified as the universal typical realization at least for small deviations from the typical current. These shocks can be stabilized by local changes in the dynamics and lead to rate functions which are independent of the system size, which have been studied before for the exclusion process. The range of accessible currents for these profiles may be limited, and we established a dynamical phase transition where large deviations for low currents are realized by condensed profiles. In this case the rate function is determined by slowing down the exit process out of the condensate which is again independent of the system size in the case of bounded rates. The transition is caused by two basic mechanisms (summarized in Figure 5.3); firstly, the range of densities in travelling wave profiles is bounded by the critical density in condensing ZRPs, this leads to a minimal accessibe current of j min = ρ/ρ c . Secondly, the
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Dynamical phase transitions in quantum mechanics

Dynamical phase transitions in quantum mechanics

Abstract. The nucleus is described as an open many-body quantum system with a non- Hermitian Hamilton operator the eigenvalues of which are complex, in general. The eigen- values may cross in the complex plane (exceptional points), the phases of the eigenfunc- tions are not rigid in approaching the crossing points and the widths bifurcate. By varying only one parameter, the eigenvalue trajectories usually avoid crossing and width bifurca- tion occurs at the critical value of avoided crossing. An analog spectroscopic redistribution takes place for discrete states below the particle decay threshold. By this means, a dynam- ical phase transition occurs in the many-level system starting at a critical value of the level density. Hence the properties of the low-lying nuclear states (described well by the shell model) and those of highly excited nuclear states (described by random ensembles) differ fundamentally from one another. The statement of Niels Bohr on the collective features of compound nucleus states at high level density is therefore not in contradiction to the shell-model description of nuclear (and atomic) states at low level density. Dynamical phase transitions are observed experimentally in different quantum mechanical systems by varying one or two parameters.
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Some properties of correlations of quantum lattice systems in thermal equilibrium

Some properties of correlations of quantum lattice systems in thermal equilibrium

Abstract. Simple proofs of uniqueness of the thermodynamic limit of KMS states and of the decay of equilibrium correlations are presented for a large class of quantum lat- tice systems at high temperatures. New quantum correlation inequalities for general Heisenberg models are described. Finally, a simplified derivation of a general result on power-law decay of correlations in 2D quantum lattice systems with continuous symme- tries is given, extending results of Mc Bryan and Spencer for the 2D classical XY model.

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Second Law and Non-Equilibrium Entropy of Schottky Systems --Doubts and Verification--

Second Law and Non-Equilibrium Entropy of Schottky Systems --Doubts and Verification--

which is used in the derivation of (1) is a special case of this relation which should be proved. Consequently, the verbal formulation of the Second Law –statements Kelvin and Clausius– cannot be transformed by the statement Carnot into Clausius inequality without a logical fallacy. A remedy may be to set (1) as an axiom, or better, to derive it in connexion with a suitable definition of a non-equilibrium entropy, a way which is worked out here serving as a motivation to have a look at this "antiquated stuff" again.

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Exponentially fast Monte Carlo simulations for non equilibrium systems

Exponentially fast Monte Carlo simulations for non equilibrium systems

The same structure of singularities is found in both of the non-equilibrium systems considered in this paper. Using the fast Monte Carlo simulations we reveal plateaus, the essentially flat regions in the probability distribution, which can be observed close to boundaries of attraction. They result from a purely dynamical effect that is not associated with the flatness of any potential. We have shown that its origin is related to switching between dif- ferent types of optimal fluctuational path, and it is a general feature of non-equilibrium systems with metastable states [Bandrivskyy et al., 2003, 2002]. The switching lines [Smelyanskiy et al., 1997] are revealed as lines along which the “global minimum of the modified action” Φ(x) exhibits sharp bends – corresponding to the predicted line at which the non-equilibrium potential is non-differentiable. In the boundary region we found the oscillations of the probability distribution and their dependence on noise intensity (see the inset in Fig.3) discussed in the recent publications [Smelyanskiy et al., 1999a; Lehmann et al., 2000; Maier and Stein, 2001]. The noise-induced shift of the singularities and the op- timal escape path revealed by the simulations has stimulated a new step in the development of the theory [Bandrivskyy et al., 2003].
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Non radiative transitions

Non radiative transitions

We c a lc u la te recom bination ra te s using two models, the Single C o n fig u ra tio n a l Coordinate Model hen cefo rth denoted by S,C,C,M, and the M olecular C ry s ta l Model h en cefo rth denoted by M,C,M, Both these models are considerably s im p lifie d versions o f the re a l systems s tu d ie d in the la b o ra to ry . However, they are b e lie v e d to contain most o f the e s s e n tia l feature s re q u ire d in the recom bination problem. One o f the p re re q u is ite s fo r the occurrence o f n o n -ra d ia tiv e tra n s itio n s is the existence o f some form o f e le c tr o n -la ttic e coup ling, In the S,C,C,M. the e le c tro n is coupled to only one lo c a l mode, w h ile in the M,C,M, the e le c tro n is coupled to a l l the c r y s ta llin e modes,
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