From Dual Unitarity to Generic Quantum Operator Spreading.

Dual-unitary circuits are paradigmatic examples of exactly solvable yet chaotic quantum many-body systems, but solvability naturally goes along with a degree of nongeneric behavior. By investigating the effect of weakly broken dual unitarity on the spreading of local operators, we study whether, and how, small deviations from dual unitarity recover fully generic many-body dynamics. We present a discrete path-integral formula for the out-of-time-order correlator and recover a butterfly velocity smaller than the light-cone velocity, v_{B}

Absence of Superdiffusion in Certain Random Spin Models.

The dynamics of spin at finite temperature in the spin-1/2 Heisenberg chain was found to be superdiffusive in numerous recent numerical and experimental studies. Theoretical approaches to this problem have emphasized the role of nonabelian SU(2) symmetry as well as integrability, but the associated methods cannot be readily applied when integrability is broken. We examine spin transport in a spin-1/2 chain in which the exchange couplings fluctuate in space and time around a nonzero mean J, a model introduced by De Nardis et al. [Phys. Rev. Lett. 127, 057201 (2021).PRLTAO0031-900710.1103/PhysRevLett.127.057201]. We show that operator dynamics in the strong noise limit at infinite temperature can be analyzed using conventional perturbation theory as an expansion in J. We find that regular diffusion persists at long times, albeit with an enhanced diffusion constant. The finite time spin dynamics is analyzed and compared with matrix product operator simulations.

Ergodic and Nonergodic Dual-Unitary Quantum Circuits with Arbitrary Local Hilbert Space Dimension.

Dual-unitary quantum circuits can be used to construct 1+1 dimensional lattice models for which dynamical correlations of local observables can be explicitly calculated. We show how to analytically construct classes of dual-unitary circuits with any desired level of (non-)ergodicity for any dimension of the local Hilbert space, and present analytical results for thermalization to an infinite-temperature Gibbs state (ergodic) and a generalized Gibbs ensemble (nonergodic). It is shown how a tunable ergodicity-inducing perturbation can be added to a nonergodic circuit without breaking dual unitarity, leading to the appearance of prethermalization plateaux for local observables.

Persistent dark states in anisotropic central spin models.

Long-lived dark states, in which an experimentally accessible qubit is not in thermal equilibrium with a surrounding spin bath, are pervasive in solid-state systems. We explain the ubiquity of dark states in a large class of inhomogeneous central spin models using the proximity to integrable lines with exact dark eigenstates. At numerically accessible sizes, dark states persist as eigenstates at large deviations from integrability, and the qubit retains memory of its initial polarization at long times. Although the eigenstates of the system are chaotic, exhibiting exponential sensitivity to small perturbations, they do not satisfy the eigenstate thermalization hypothesis. Rather, we predict long relaxation times that increase exponentially with system size. We propose that this intermediate chaotic but non-ergodic regime characterizes mesoscopic quantum dot and diamond defect systems, as we see no numerical tendency towards conventional thermalization with a finite relaxation time.

Floquet-Engineering Counterdiabatic Protocols in Quantum Many-Body Systems.

Counterdiabatic (CD) driving presents a way of generating adiabatic dynamics at an arbitrary pace, where excitations due to nonadiabaticity are exactly compensated by adding an auxiliary driving term to the Hamiltonian. While this CD term is theoretically known and given by the adiabatic gauge potential, obtaining and implementing this potential in many-body systems is a formidable task, requiring knowledge of the spectral properties of the instantaneous Hamiltonians and control of highly nonlocal multibody interactions. We show how an approximate gauge potential can be systematically built up as a series of nested commutators, remaining well defined in the thermodynamic limit. Furthermore, the resulting CD driving protocols can be realized up to arbitrary order without leaving the available control space using tools from periodically driven (Floquet) systems. This is illustrated on few- and many-body quantum systems, where the resulting Floquet protocols significantly suppress dissipation and provide a drastic increase in fidelity.

Spin Polarization through Floquet Resonances in a Driven Central Spin Model.

Adiabatically varying the driving frequency of a periodically driven many-body quantum system can induce controlled transitions between resonant eigenstates of the time-averaged Hamiltonian, corresponding to adiabatic transitions in the Floquet spectrum and presenting a general tool in quantum many-body control. Using the central spin model as an application, we show how such controlled driving processes can lead to a polarization-based decoupling of the central spin from its decoherence-inducing environment at resonance. While it is generally impossible to obtain the exact Floquet Hamiltonian in driven interacting systems, we exploit the integrability of the central spin model to show how techniques from quantum quenches can be used to explicitly construct the Floquet Hamiltonian in a restricted many-body basis and model Floquet resonances.

Analysis of initial slow waves (ISWs) at the seizure onset in patients with drug resistant temporal lobe epilepsy.

RATIONALE: The goal of this study is to analyze initial slow waves (ISWs) at seizure onset in patients with refractory temporal lobe epilepsy. ISWs are a specific type of ictal EEG pattern characterized by a slow wave at the seizure onset followed by low voltage fast activity. METHODS: Investigations were carried out on 14 patients from the UCLA hospital (USA) and 10 from the Ghent University Hospital (Belgium) implanted with depth and grid electrodes for localization of the epileptogenic zone. RESULTS: Sixty-one seizures in the UCLA group and 30 seizures in the Ghent group were analyzed. Fourteen UCLA and seven Ghent patients had ISWs at seizure onset. The duration of ISWs varied between 0.3 to 6.0 s and maximum amplitude varied from 0.2 to 1.4 mV. ISWs in three of 14 UCLA patients (30% of seizures) had a consistent positive polarity at the deepest contacts that were located in the amygdala, hippocampus, or entorhinal cortex and reversed polarity outside of these brain areas (ISWs1). ISWs in 11 of 14 UCLA patients (70% of seizures) had negative polarity at the deepest electrodes and their amplitude increased toward the recording contacts located in the white matter or neocortex (ISWs2). All ISWs from the seven Ghent patients were negative in the depth contacts (ISWs2) and positive on grid electrodes at the cortical surface. ISWs1 were associated with EEG spikes at the onset and on increase in amplitude of 10-20 Hz sinusoidal activity. In contrast, ISWs2 were associated with suppression of EEG amplitude, an increase in frequency in the range of 20-50 Hz, and did not have EEG spikes at the onset. Multiunit neuronal activity showed strong synchronization of neuronal discharges during interictal spikes, but multiunit synchronization was not obvious during ISWs2. CONCLUSION: The existence of EEG spikes and phase reversal with ISWs1 indicates this type of seizure may be triggered by hypersynchronous neuronal discharges; however, seizures with ISWs2 at the onset may be triggered by different mechanisms, perhaps nonneuronal.

High frequency deep brain stimulation in the hippocampus modifies seizure characteristics in kindled rats.

PURPOSE: This experimental animal study evaluates the effect of high frequency deep brain stimulation (HFS DBS) on seizures in the Alternate Day Rapid Kindling model for temporal lobe epilepsy (TLE). The target for HFS is the hippocampus, as this structure is often presumed to be the seizure focus in human TLE. METHODS: Rats (n = 12) were fully kindled in the hippocampus according to the Alternate Day Rapid Kindling protocol. Characteristics of the evoked afterdischarges (AD) were determined in the baseline period using AD threshold, AD latency, and AD duration as parameters. Rats were divided into a treated group (n = 7) that received 130 Hz HFS for 1 week, and a control group (n = 5) that did not receive HFS. Rats were retested in the following week. After 1 additional week of rest, the HFS group was continuously stimulated again for 1 week, during which AD evoked by kindling stimuli were characterized again. RESULTS: HFS had a direct effect on evoked AD: during HFS, it increased AD threshold to 203 +/- 13% of controls (p < 0.01) and increased AD latency to 191 +/- 19% (p < 0.05). It decreased AD duration to 71 +/- 9% (p < 0.05) of controls. The effect outlasted the HFS stimulation as in the week following HFS similar differences, but smaller in size, could still be established. CONCLUSION: Continuous HFS (130 Hz) in the hippocampus of epileptic rats modulates the characteristics of evoked AD in a way that reflects a reduction in excitability of the target region.

Rapid kindling in preclinical anti-epileptic drug development: the effect of levetiracetam.

PURPOSE: This study assesses the use of the serial day Rapid Kindling with Recurrent Hippocampal Seizures (RKRHS) model in drug testing by investigating the anti-epileptic effect of levetiracetam (LEV), a novel anti-epileptic drug (AED) with a unique preclinical profile. METHODS: Male Wistar rats (n=16) were implanted with a stimulation/recording electrode unit in the right hippocampus and epidural recording electrodes. One week later, all rats received 12 stimulations each day for several consecutive days according to the serial day RKRHS protocol, until they were fully kindled. Fully kindled rats were then randomly assigned to an active (n=8) and a control (n=6) group and injected once (intraperitoneal, i.p.) with levetiracetam (54 mg/kg) or saline (0.9% NaCl, 2 ml/kg), respectively. One hour later, the rats received additional kindling stimulations, during which the effect of LEV was assessed. RESULTS: One hour following injection of LEV, mean seizure stage dropped to 1.67+/-1.03 compared to 5+/-0 in controls (p<0.05). Mean ADD was also significantly shorter in the active group than in controls; 21.16+/-5.03 s versus 57.24+/-8.16s, respectively (p<0.05). A gradual, time-dependent decline was noted in the anti-epileptic effect of LEV but this effect stayed statistically significant at least up to 2.5 h (p<0.05). CONCLUSION: LEV was demonstrated to have anti-epileptic properties in RKRHS that compared to those in traditional kindling and contrast with results from classical screening tests. RKRHS may represent a valuable and sensitive screening tool early in the drug screening process.

Chronic levetiracetam treatment early in life decreases epileptiform events in young GAERS, but does not prevent the expression of spike and wave discharges during adulthood.

PURPOSE: In Genetic Absence Epilepsy Rats from Strasbourg (GAERS), age-related absence seizures start to appear from postnatal day (PN) 30 concomitant with 'spike and wave discharges' (SWDs) appearing on cortical EEG recordings. The aim of this study was to investigate the effect of early chronic levetiracetam (LEV) treatment on the development of SWDs in young and adult GAERS. METHODS: From PN 23 until PN 60, LEV (54 mg/kg, i.p.) was administered once daily to GAERS (n=8), while control GAERS (n=7) received saline (0.9% NaCl, i.p.). All animals were implanted with four epidural EEG electrodes at PN 51. EEG was recorded for 3h daily, during the last 4 days of the treatment (PN 57-PN 60) and during 4 additional days after treatment had been terminated (PN 61-PN 64). The animals were monitored again at the age of 4 months (PN 120-PN 124), about 2 months after the last administration of LEV. RESULTS: During treatment, epileptiform events in the LEV group were significantly reduced (62%, P<0.05) in comparison with the control group. During the following 4 days, epileptiform events were reduced in the LEV group, with an average difference of 53% (P=0.064). Once the animals had reached adult age, there was no difference in epileptiform events between the LEV group and controls. CONCLUSION: In this study, chronic LEV administration induced a reduction in epileptiform events in young GAERS. This effect persisted to some extent after treatment cessation (PN 61-PN 64), which might indicate a slowing down of epileptogenic processes. However, at the age of 4 months all animals revealed a similar expression of epileptiform discharges.

Generator replacement in epilepsy patients treated with vagus nerve stimulation.

PURPOSE: In epilepsy patients treated with vagus nerve stimulation (VNS), the occurrence of end of battery life (EOBL), when the generator will no longer deliver any stimulation, was investigated with regard to seizure control. EOBL is preceeded by end of effective stimulation (EOES) when irregular stimulation may occur. METHODS: In 14/78 patients, treated with VNS at Ghent University Hospital, generators were replaced at different times following EOES or EOBL. We retrospectively analysed the time of occurrence of EOES and EOBL and seizure control before and after generator replacement. RESULTS: EOES or EOBL was indicated by loss of seizure control, decreased perception of stimulation and recurrence of depression in 3, 3 and 1/14 patient(s), respectively. In 2 and 1/14 patient(s), EOBL and premature generator failure, respectively, were detected during routine check-up at the epilepsy clinic. In 4/14 patients, generator replacement was performed before estimated EOES. Pre-replacement seizure control could not be regained in 2/14 patients in whom replacement had been postponed for several months. Estimation of EOES and EOBL occurrence proved difficult in individual patients. CONCLUSION: EOES or EOBL may be indicated by loss of seizure control, decreased or irregular perception of stimulation by the patient and loss of other VNS-induced effects. Postponing generator replacement may result into permanent loss of seizure control. In responders we suggest generator replacement before EOBL. Our results call for performance of prospective studies in larger patient groups that may eventually lead to general guidelines on the indication and timing of generator replacement.

Acute vagus nerve stimulation does not suppress spike and wave discharges in genetic absence epilepsy rats from Strasbourg.

We evaluated the efficacy of vagus nerve stimulation (VNS) in Genetic Absence Epilepsy Rats from Strasbourg (GAERS), a validated model for absence epilepsy. In the first experiment, we investigated whether VNS applied at seizure onset can interrupt spike and wave discharges (SWD). In the second experiment, we investigated whether SWD are suppressed or shortened in duration when VNS is applied several hours per day. Both control and VNS groups underwent EEG and VNS electrode implantation. For the first experiment, a randomized crossover design was used. Stimuli (amplitude: 3 V; frequency: 30 Hz; pulse duration: 500 micros) were given when an SWD occurred on the EEG. The experiment was repeated the next day. In the second experiment, treated animals were stimulated (amplitude: 1.5 mA; frequency: 30 Hz; pulse duration: 500 micros; on/off time cycle: 30 s / 5 min) for 3h per day, during five consecutive days. In the first experiment, the duration of the SWD was increased on day 1, (P < 0.05). There was no difference in SWD duration on Day 2. In the second experiment, no significant differences could be found in number, duration and EEG frequency of SWD. VNS applied at the onset of an SWD can prolong the duration of SWD in GAERS. As a 5-day stimulation protocol had no effect, long-term VNS might be necessary to affect SWD.

Enterocolitis: an adverse event in refractory epilepsy patients treated with levetiracetam?

INTRODUCTION: Levetiracetam (LEV) is a recently marketed novel anti-epileptic drug with a promising efficacy and safety profile. In this report we describe two patients who presented with enterocolitis and discuss the possible relationship with concurrent LEV intake. PATIENTS: In two patients. LEV was initiated to control refractory complex partial seizures (CPS). The first patient was treated with 1500 mg/day and complained of abdominal pain and weight loss 6 months later. Internal examination and colonoscopy revealed a punctate colitis. The second patient presented with bloody stool 1 month after LEV initiation. Colonoscopy showed punctate colitis. In both patients gastrointestinal symptoms disappeared following tapering of LEV. DISCUSSION: There are no reports in the literature describing colitis related to LEV intake. Three possible mechanisms of action are discussed. Colitis may be part of a hypersensitivity syndrome caused by LEV. Pharmacodynamic interactions with other anti-epileptic drugs, for example, carbamazepine may play a role. A haematological adverse event is another possibility since piracetam, a related molecule, has a known impact on erythrocytes and platelets. CONCLUSION: The close temporal relationship between initiation of LEV intake, symptomatic colitis and clinical improvement following LEV tapering, suggests that colitis may be a possible and previously undescribed adverse effect of LEV.

Neurostimulation for refractory epilepsy.

Neurostimulation is an emerging treatment for refractory epilepsy. To date the precise mechanism of action remains to be elucidated. Better insight in the mechanism of action may identify seizure types or syndromes that respond to such a treatment and may guide the search for optimal stimulation parameters and finally improve clinical efficacy. In the past ten years some progress has been made through neurophysiological, neuroanatomical, neurochemical and cerebral blood flow studies in patients and animals undergoing vagus nerve stimulation (VNS). Interesting results have been found in VNS-treated patients that underwent evoked potential measurements, cerebrospinal fluid investigation, neuropsychological testing and PET, SPECT and fMRI testing. Desynchronisation of abnormal synchronous epileptic activity is one of the hypotheses on the mode of action that might primarily be responsible for an anti-seizure effect. There is however increasing evidence from research and clinical observation that VNS might establish a true and long-term anti-epileptic effect. It has been shown that VNS influences neurotransmission in the brain and provokes long-term changes in cerebral blood flow in areas crucial for epileptogenesis such as the thalamus and medial temporal lobe structures. Deep brain stimulation (DBS) for epilepsy has regained interest. Central nervous system structures known to play a key role in the epileptogenic network such as the thalamus and subthalamic nucleus have been targeted. Another approach is to target the ictal onset zone such as the medial temporal lobe. At Ghent University Hospital 10 patients have been treated with long-term amygdalohippocampal DBS. Several hypotheses have been raised for the mechanism of action of DBS for refractory seizures. Seizure reduction may be due to a microlesion caused by electrode insertion or by provoking a reversible functional lesion due to the effect of electrical current on hyperexcitable tissue. Neurophysiological techniques such as evoked potentials monitoring and intraoperative single unit potential recordings may guide correct electrode placement, individual DBS titration and elucidation of the mechanims of action of DBS for epilepsy.