Tankut Can

• The Graduate Center

Computations involved in processes such as decision-making, working memory, and motor control are thought to emerge from the dynamics governing the collective activity of neurons in large populations. But the estimation of these dynamics remains a significant challenge. Here we introduce Flow-field Inference from Neural Data using deep Recurrent ne...

Understanding how the dynamics in biological and artificial neural networks implement the computations required for a task is a salient open question in machine learning and neuroscience. In particular, computations requiring complex memory storage and retrieval pose a significant challenge for these networks to implement or learn. Recently, a fami...

Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) and neuroscience. Prior theoretical work has focused on RNNs with additive interactions. However, gating, i.e., multiplicative, interactions are ubiquitous in real neurons and also the central feature of the best-performing RNNs in ML. Here, we show...

The ability to store continuous variables in the state of a biological system (e.g. a neural network) is critical for many behaviours. Most models for implementing such a memory manifold require hand-crafted symmetries in the interactions or precise fine-tuning of parameters. We present a general principle that we refer to as {\it frozen stabilisat...

The study of dissipation and decoherence in generic open quantum systems recently led to the investigation of spectral and steady-state properties of random Lindbladian dynamics. A natural question is then how realistic and universal those properties are. Here, we address these issues by considering a different description of dissipative quantum sy...

We consider an isotropic compressible nondissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid and the free surface boundary conditions depend explicitly on the parity-breaking nondissipative odd viscosity term. We construct an...

RNNs are popular dynamical models, used for processing sequential data. Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions, where the input to a unit is a weighted sum of the output of the remaining units in network. However, there is ample evidence that neurons can have gating - i.e. mul...

The study of dissipation and decoherence in generic open quantum systems recently led to the investigation of spectral and steady-state properties of random Lindbladian dynamics. A natural question is then how realistic and universal those properties are. Here, we address these issues by considering a different description of dissipative quantum sy...

Recurrent neural networks (RNNs) are powerful dynamical models for data with complex temporal structure. However, training RNNs has traditionally proved challenging due to exploding or vanishing of gradients. RNN models such as LSTMs and GRUs (and their variants) significantly mitigate the issues associated with training RNNs by introducing various...

We discuss the decay rates of chaotic quantum systems coupled to noise. We model both the Hamiltonian and the system-noise coupling by random N×N Hermitian matrices, and study the spectral properties of the resulting Liouvillian superoperator. We consider various random-matrix ensembles, and find that for all of them the asymptotic decay rate remai...

We study the mixing behavior of random Lindblad generators with no symmetries, using the dynamical map or propagator of the dissipative evolution. In particular, we determine the long-time behavior of a dissipative form factor, which is the trace of the propagator, and use this as a diagnostic for the existence or absence of a spectral gap in the d...

We consider an isotropic compressible non-dissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid as well as the free surface boundary conditions depend explicitly on the parity breaking non-dissipative odd viscosity term. We con...

We discuss the decay rates of chaotic quantum systems coupled to noise. We model both the Hamiltonian and the system-noise coupling by random $N \times N$ Hermitian matrices, and study the spectral properties of the resulting Lindblad superoperator. We consider various random-matrix ensembles, and find that for all of them the asymptotic decay rate...

We study the mixing behavior of random Lindblad generators with no symmetries, using the dynamical map or propagator of the dissipative evolution. In particular, we determine the long-time behavior of a dissipative form factor, which is the trace of the propagator, and use this as a diagnostic for the existence or absence of a spectral gap in the d...

The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it changes its "knottedness"; and no deformation of a closed surface, short of puncturing it, changes how many ha...

We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken. For the case of incompressible fluids, the odd viscosity manifests itself through the free surface (no stress...

DOI:https://doi.org/10.1103/PhysRevLett.120.089903

The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it changes its "knottedness"; and no deformation of a closed surface, short of puncturing it, changes how many ha...

We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken. For the case of incompressible fluids, the odd viscosity manifests itself through the free surface (no stress...

In [Can et al. 2016], quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic adiabatic states, which we define in the paper. We highlight the connection between the universal features of geometr...

In [Can et al. 2016], quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic adiabatic states, which we define in the paper. We highlight the connection between the universal features of geometr...

DOI:https://doi.org/10.1103/PhysRevLett.118.269902

We study quantum Hall (QH) states on a punctured Riemann sphere. We compute the Berry curvature under adiabatic motion in the moduli space in the large N limit. The Berry curvature is shown to be finite in the large N limit and controlled by the conformal dimension of the cusp singularity, a local property of the mean density. Utilizing exact sum r...

We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various Berry phases, and the static structure factor of PH-conjugate states from the corresponding proper...

We study quantum Hall states on surfaces with conical singularities. We show that the electronic fluid at the cone tip possesses an intrinsic angular momentum, which is due solely to the gravitational anomaly. We also show that quantum Hall states behave as conformal primaries near singular points, with a conformal dimension equal to the angular mo...

We derive a number of exact relations between response functions of holomorphic, chiral fractional quantum Hall states and their particle-hole (PH) conjugates. These exact relations allow one to calculate the Hall conductivity, Hall viscosity, various Berry phases, and the static structure factor of PH-conjugate states from the corresponding proper...

We show that quantum Hall states on surfaces with conical singularities behave as conformal primaries near the singular points, with a conformal dimension controlled by the gravitational anomaly. We show that the electronic fluid at the cone tip possesses an intrinsic angular momentum equal to the conformal dimension, in units of the Planck constan...

We develop a collective field theory for fractional quantum Hall (FQH) states. We show that in the leading approximation for a large number of particles, the properties of Laughlin states are captured by a Gaussian free field theory with a (filling fraction dependent) background charge. Gradient corrections to the Gaussian field theory arise from u...

We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local trans...

We develop a field theory description of fractional quantum Hall (FQH) states. We show that in the leading approximation in a gradient expansion, Laughlin states are described by a Gaussian free field theory with a background charge which is identified with the anomalous viscosity of the states. The background charge increases the central charge of...

We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local trans...

We develop a general method to compute correlation functions of fractional quantum Hall (FQH) states on a curved space. In a curved space, local transformation properties of FQH states are examined through local geometric variations, which are essentially governed by the gravitational anomaly. Furthermore, we show that the electromagnetic response...

Long-lived coherences have been observed in photosynthetic complexes after laser excitation, inspiring new theories regarding the extreme quantum efficiency of photosynthetic energy transfer. Whether coherent (ballistic) transport occurs in nature and whether it improves photosynthetic efficiency remain topics of debate. Here, we use a non-equilibr...

Using the non-equilibrium Keldysh Green's function formalism, we investigate the local, non-equilibrium charge transport in graphene nanoribbons (GNRs). In particular, we demonstrate that the spatial current patterns associated with discrete transmission resonances sensitively depend on the GNRs' geometry, size, and aspect ratio, the location and n...

There is a well known analogy between the Laughlin trial wave function for the fractional quantum Hall effect, and the Boltzmann factor for the two-dimensional one-component plasma. The latter requires analytic continuation beyond the finite geometry used in its derivation. We consider both disk and cylinder geometry, and focus attention on the exa...

A distinguishing feature of Fractional Quantum Hall states is a singular behavior of equilibrium densities at boundaries. In contrast to states at integer filling fraction, such quantum liquids posses an additional dipole moment localized near edges. It enters observable quantities such as universal dispersion of edge states and Lorentz shear stres...

We propose a new method for atomic-scale imaging of spatial current patterns in nanoscopic quantum networks by using scanning tunneling microscopy (STM). By measuring the current flowing from the STM tip into one of the leads attached to the network as a function of tip position, one obtains an atomically resolved spatial image of "current riverbed...

Using the non-equilibrium Keldysh Green's function formalism, we show that the non-equilibrium charge transport in nanoscopic quantum networks takes place via {\it current eigenmodes} that possess characteristic spatial patterns. We identify the microscopic relation between the current patterns and the network's electronic structure and topology an...

Using the Keldysh Green's function formalism, we study the non-equilibrium charge transport in nanoscopic quantum networks [1]. Due to quantum confinement, charge transport takes place via current eigenmodes that possess characteristic spatial patterns of current paths. In the ballistic limit, these patterns exhibit unexpected features such as curr...