Ядерная спиновая динамика и флуктуации в анизотропной модели большого ящика

We consider the central spin model in the box approximation taking into account an external magnetic field and the anisotropy of the hyperfine interaction. From the exact Hamiltonian diagonalization we obtain analytical expressions for the nuclear spin dynamics in the limit of many nuclear spins. We predict the nuclear spin precession in zero magnetic field for the case of the anisotropic interaction between electron and nuclear spins. We calculate and describe the nuclear spin noise spectra in the thermodynamic equilibrium. The obtained results can be used for the analysis of the nuclear spin induced current fluctuations in organic semiconductors.

Asynchronous and Coherent Dynamics in Balanced Excitatory-Inhibitory Spiking Networks

Dynamic excitatory-inhibitory (E-I) balance is a paradigmatic mechanism invoked to explain the irregular low firing activity observed in the cortex. However, we will show that the E-I balance can be at the origin of other regimes observable in the brain. The analysis is performed by combining extensive simulations of sparse E-I networks composed of N spiking neurons with analytical investigations of low dimensional neural mass models. The bifurcation diagrams, derived for the neural mass model, allow us to classify the possible asynchronous and coherent behaviors emerging in balanced E-I networks with structural heterogeneity for any finite in-degree K. Analytic mean-field (MF) results show that both supra and sub-threshold balanced asynchronous regimes are observable in our system in the limit N >> K >> 1. Due to the heterogeneity, the asynchronous states are characterized at the microscopic level by the splitting of the neurons in to three groups: silent, fluctuation, and mean driven. These features are consistent with experimental observations reported for heterogeneous neural circuits. The coherent rhythms observed in our system can range from periodic and quasi-periodic collective oscillations (COs) to coherent chaos. These rhythms are characterized by regular or irregular temporal fluctuations joined to spatial coherence somehow similar to coherent fluctuations observed in the cortex over multiple spatial scales. The COs can emerge due to two different mechanisms. A first mechanism analogous to the pyramidal-interneuron gamma (PING), usually invoked for the emergence of γ-oscillations. The second mechanism is intimately related to the presence of current fluctuations, which sustain COs characterized by an essentially simultaneous bursting of the two populations. We observe period-doubling cascades involving the PING-like COs finally leading to the appearance of coherent chaos. Fluctuation driven COs are usually observable in our system as quasi-periodic collective motions characterized by two incommensurate frequencies. However, for sufficiently strong current fluctuations these collective rhythms can lock. This represents a novel mechanism of frequency locking in neural populations promoted by intrinsic fluctuations. COs are observable for any finite in-degree K, however, their existence in the limit N >> K >> 1 appears as uncertain.

Current Fluctuations in Hybrid-Superconductor Normal Structures with Quantum Dots

<p>Nanostructures with quantum dots in proximity to superconducting electrodes are an ideal tool to study superconducting correlations in systems with few degrees of freedom that exhibit strong Coulomb-interaction effects. Such hybrid superconductor-normal structures show rich physics due to the interplay of superconductivity, Coulomb interaction and non-equilibrium. Superconducting correlations are established on the quantum dot when it is coupled to a superconductor even in the presence of strong Coulomb repulsion and Cooper pairs can tunnel coherently between the quantum dot and the superconductor. In this thesis, we investigate theoretically electronic transport through an interacting quantum dot coupled to normal and superconducting leads. The presence of the proximity effect can be detected by the dot's current, namely the Andreev current. However, current fluctuations might reveal information on the electronic transport and the internal structure of the system which is not visible in the mean value of the current. For this reason, we study the current fluctuations through the proximized quantum dot to get access to the properties of such a hybrid quantum-dot system. In particular, we are interested in the finite-frequency fluctuations to unveil the coherent dynamics underlying the proximity effect in the quantum dot and its internal time scales. At first, we present a study of the frequency-dependent current noise for subgap transport through an interacting single-level quantum dot tunnel-coupled to normal and superconducting leads. For this purpose, we employ a non-equilibrium diagrammatic real-time approach to calculate the finite-frequency current noise. The finite-frequency noise spectrum shows a sharp dip at a frequency corresponding to the energy splitting of the Andreev bound states which is a signature of the coherent exchange of Cooper pairs between the quantum dot and the superconductor. Furthermore, in the high frequency regime, the so called quantum noise regime, the noise spectrum exhibits steps at frequencies equal to the excitation energies. These steps can be related to the effective coupling strength of the excitations. However, the statistical description of the electron transport does not stop with the noise. Current cumulants of arbitrary order can be obtained by means of full counting statistics (FCS). We set up a theory based on the diagrammatic real-time approach to calculate the finite-time FCS for quantum transport with a non-Markovian master equation that captures the initial correlations between system and reservoir. This allows us to fully describe the current fluctuations of the hybrid quantum-dot system, that is the noise and all higher order current cumulants.</p>

Current Fluctuations in Hybrid-Superconductor Normal Structures with Quantum Dots

<p>Nanostructures with quantum dots in proximity to superconducting electrodes are an ideal tool to study superconducting correlations in systems with few degrees of freedom that exhibit strong Coulomb-interaction effects. Such hybrid superconductor-normal structures show rich physics due to the interplay of superconductivity, Coulomb interaction and non-equilibrium. Superconducting correlations are established on the quantum dot when it is coupled to a superconductor even in the presence of strong Coulomb repulsion and Cooper pairs can tunnel coherently between the quantum dot and the superconductor. In this thesis, we investigate theoretically electronic transport through an interacting quantum dot coupled to normal and superconducting leads. The presence of the proximity effect can be detected by the dot's current, namely the Andreev current. However, current fluctuations might reveal information on the electronic transport and the internal structure of the system which is not visible in the mean value of the current. For this reason, we study the current fluctuations through the proximized quantum dot to get access to the properties of such a hybrid quantum-dot system. In particular, we are interested in the finite-frequency fluctuations to unveil the coherent dynamics underlying the proximity effect in the quantum dot and its internal time scales. At first, we present a study of the frequency-dependent current noise for subgap transport through an interacting single-level quantum dot tunnel-coupled to normal and superconducting leads. For this purpose, we employ a non-equilibrium diagrammatic real-time approach to calculate the finite-frequency current noise. The finite-frequency noise spectrum shows a sharp dip at a frequency corresponding to the energy splitting of the Andreev bound states which is a signature of the coherent exchange of Cooper pairs between the quantum dot and the superconductor. Furthermore, in the high frequency regime, the so called quantum noise regime, the noise spectrum exhibits steps at frequencies equal to the excitation energies. These steps can be related to the effective coupling strength of the excitations. However, the statistical description of the electron transport does not stop with the noise. Current cumulants of arbitrary order can be obtained by means of full counting statistics (FCS). We set up a theory based on the diagrammatic real-time approach to calculate the finite-time FCS for quantum transport with a non-Markovian master equation that captures the initial correlations between system and reservoir. This allows us to fully describe the current fluctuations of the hybrid quantum-dot system, that is the noise and all higher order current cumulants.</p>

Critical current fluctuations in graphene Josephson junctions

We have studied 1/f noise in critical current $$I_c$$ I c in h-BN encapsulated monolayer graphene contacted by NbTiN electrodes. The sample is close to diffusive limit and the switching supercurrent with hysteresis at Dirac point amounts to $$\simeq 5$$ ≃ 5 nA. The low frequency noise in the superconducting state is measured by tracking the variation in magnitude and phase of a reflection carrier signal $$v_{rf}$$ v rf at 600–650 MHz. We find 1/f critical current fluctuations on the order of $$\delta I_c/I_c \simeq 10^{-3}$$ δ I c / I c ≃ 10 - 3 per unit band at 1 Hz. The noise power spectrum of critical current fluctuations $$S_{I_c}$$ S I c measured near the Dirac point at large, sub-critical rf-carrier amplitudes obeys the law $$S_{I_c}/{I{_c}}^2 = a/f^{\beta }$$ S I c / I c 2 = a / f β where $$a\simeq 4\times 10^{-6}$$ a ≃ 4 × 10 - 6 and $$\beta \simeq 1$$ β ≃ 1 at $$f > 0.1$$ f > 0.1 Hz. Our results point towards significant fluctuations in $$I_c$$ I c originating from variation of the proximity induced gap in the graphene junction.

Asynchronous and coherent dynamics in balanced excitatory-inhibitory populations

Dynamic excitatory-inhibitory (E-I) balance is a paradigmatic mechanism invoked to explain the irregular low firing activity observed in the cortex. However, we will show that the E-I balance can be at the origin of other regimes observable in the brain. The analysis is performed by combining extensive simulations of sparse E-I networks composed of N spiking neurons with analytical investigations of low dimensional neural mass models. The bifurcation diagrams, derived for the neural mass model, allow to classify the possible asynchronous and coherent behaviours emerging in balanced E-I networks with structural heterogeneity for any finite in-degree K. In the limit N >> K >> 1 both supra and sub-threshold balanced asynchronous regimes can be observed in our system. Due to the heterogeneity the asynchronous states are characterized by the splitting of the neurons in three groups: silent, fluctuation and mean driven. These features are consistent with experimental observations reported for heterogeneous neural circuits. The coherent rhythms observed in our system can range from periodic and quasi-periodic collective oscillations (COs) to coherent chaos. These rhythms are characterized by regular or irregular temporal fluctuations joined to spatial coherence somehow similar to coherent fluctuations observed in the cortex over multiple spatial scales. The COs can emerge due to two different mechanisms. A first mechanism similar to the pyramidal-interneuron gamma (PING) one, usually invoked for the emergence of gamma-oscillations. The second mechanism is intimately related to the presence of current fluctuations, which sustain COs characterized by an essentially simultaneous bursting of the two populations. We observe period-doubling cascades involving the PING-like COs finally leading to the appearance of coherent chaos. Fluctuation driven COs are usually observable in our system as quasi-periodic collective motions characterized by two incommensurate frequencies. However, for sufficiently strong current fluctuations we report a novel mechanism of frequency locking among collective rhythms promoted by these intrinsic fluctuations. Our analysis suggest that despite PING-like or fluctuation driven COS are observable for any finite in-degree K, in the limit N >> K >> 1 these solutions finally result in two coexisting balanced regimes: an asynchronous and a fully synchronized one.

Time-dependent expression of ryanodine receptors in sea urchin eggs, zygotes and early embryos

Summary In this work, the presence of calcium-dependent calcium channels and their receptors (RyR) has been investigated in Paracentrotus lividus eggs and early embryos, from unfertilized egg to four-blastomere stages. Electrophysiological recordings of RyR single-channel current fluctuations showed that RyRs are functional during the first developmental events with a maximum at zygote stage, c. 40 min after fertilization, corresponding to the first cleavage. The nature of vertebrate-like RyRs active at this stage was established by specific activation/blockade experiments.