$Circuit~ Complexity$, a well known computational technique has recently become the backbone of the physics community to probe the chaotic behaviour and random quantum fluctuations of quantum fields. This paper is devoted to the study of out-of-equilibrium aspects and quantum chaos appearing in the universe from the paradigm of two well known bouncing cosmological solutions viz. $Cosine~ hyperbolic$ and $Exponential$ models of scale factors. Besides $circuit~ complexity$, we use the $Out-of-Time~ Ordered~ correlation~ (OTOC)$ functions for probing the random behaviour of the universe both at early and the late times. In particular, we use the techniques of well known two-mode squeezed state formalism in cosmological perturbation theory as a key ingredient for the purpose of our computation. To give an appropriate theoretical interpretation that is consistent with the observational perspective we use the scale factor and the number of e-foldings as a dynamical variable instead of conformal time for this computation. From this study, we found that the period of post bounce is the most interesting one. Though it may not be immediately visible, but an exponential rise can be seen in the $complexity$ once the post bounce feature is extrapolated to the present time scales. We also find within the very small acceptable error range a universal connecting relation between Complexity computed from two different kinds of cost functionals-$linearly~ weighted$ and $geodesic~ weighted$ with the OTOC. Furthermore, from the $complexity$ computation obtained from both the cosmological models and also using the well known MSS bound on quantum Lyapunov exponent, $\lambda\leq 2\pi/\beta$ for the saturation of chaos, we estimate the lower bound on the equilibrium temperature of our universe at late time scale. Finally, we provide a rough estimation of the scrambling time in terms of the conformal time.

/pdf/quantum-aspects-of-chaos-and-complexity-from-bouncing-1mhdvflokh.pdf

Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism

In this article, we investigate the quantum circuit complexity and entanglement entropy in the recently studied black hole gas framework using the two-mode squeezed states formalism written in arbitrary dimensional spatially flat cosmological Friedmann-Lemaitre-Robertson-Walker background space-time. We compute the various complexity measures and study the evolution of these complexities by following two different prescriptions viz the covariant matrix method and Nielsen’s method. Independently, using the two-mode squeezed states formalism we also compute the Renyi and von-Neumann entanglement entropy, which show an inherent connection between the entanglement entropy and quantum circuit complexity. We study the behavior of the complexity measures and entanglement entropy separately for three different spatial dimensions and observe various significant different features in three spatial dimensions on the evolution of these quantities with respect to the scale factor. Furthermore, we also study the underlying behavior of the equilibrium temperature with two of the most essential quantities i.e., rate of change of complexity with scale factor and the entanglement entropy. We observe that irrespective of the spatial dimension, the equilibrium temperature depends quartically on entanglement entropy.

Circuit complexity as a novel probe of quantum entanglement: A study with black hole gas in arbitrary dimensions

In this paper, we explore the connection between the curvature of the background De Sitter space-time with the spectroscopic study of entanglement of two atoms. Our set up is in the context of an Open Quantum System (OQS), where the two atoms, each having two energy levels and represented by Pauli spin tensor operators projected along any arbitrary direction. The system mimics the role of a pair of freely falling Unruh De-Witt detectors, which are allowed to non-adiabatically interact with a conformally coupled massless probe scalar field which has the role of background thermal bath. The effective dynamics of this combined system takes into account of the non-adiabatic interaction, which is commonly known as the Resonant Casimir Polder Interaction (RCPI) with the thermal bath. Our analysis reveals that the RCPI of two stable entangled atoms in the quantum vacuum states in OQS depends on the de Sitter space-time curvature relevant to the temperature of the thermal bath felt by the static observer. We also find that, in OQS, RCPI produces a new significant contribution appearing in the effective Hamiltonian of the total system and thermal bath under consideration. We find that the Lamb Shift is characterized by a decreasing inverse square power-law behavior, $L^{-2}$, when inter atomic Euclidean distance, $L$, is much larger than a characteristic length scale, $k$, which is the inverse surface gravity of the background De Sitter space. If the background space-time would have been Minkowskian this shift decreases as, $L^{-1}$, and is independent of temperature. Thus, we establish a connection between the curvature of the De Sitter space-time with the Lamb Shift spectroscopy.

/pdf/relating-the-curvature-of-de-sitter-universe-to-open-quantum-284sznny6s.pdf

Relating the curvature of De Sitter Universe to Open Quantum Lamb Shift Spectroscopy

Circuit Complexity, a well known computational technique has recently become the backbone of the physics community to probe the chaotic behaviour and random quantum fluctuations of quantum fields. This paper is devoted to the study of out-of-equilibrium aspects and quantum chaos appearing in the universe from the paradigm of two well known bouncing cosmological solutions viz. Cosine hyperbolic and Exponential models of scale factors. Besides circuit complexity, we use the Out-of-Time Ordered correlation (OTOC) functions for probing the random behaviour of the universe both at early and the late times. In particular, we use the techniques of well known two-mode squeezed state formalism in cosmological perturbation theory as a key ingredient for the purpose of our computation. To give an appropriate theoretical interpretation that is consistent with the observational perspective we use the scale factor and the number of e-foldings as a dynamical variable instead of conformal time for this computation. From this study, we found that the period of post bounce is the most interesting one. Though it may not be immediately visible but an exponential rise can be seen in the complexity once the post bounce feature is extrapolated to the present time scales. We also find within the very small acceptable error range a universal connecting relation between Complexity computed from two different kinds of cost functionals-linearly weighted and geodesic weighted with the OTOC. Furthermore, from the complexity computation obtained from both the cosmological models under consideration and also using the well known Maldacena (M) Shenker (S) Stanford (S) bound on quantum Lyapunov exponent, λ ≤ 2π/β for the saturation of chaos, we estimate the lower bound on the equilibrium temperature of our universe at the late time scale. Finally, we provide a rough estimation of the scrambling time scale in terms of the conformal time.

/pdf/quantum-aspects-of-chaos-and-complexity-from-bouncing-59smz6xrze.pdf

The Internet of Things era has promoted enormous research on sensors, communications, data fusion, and actuators. Among them, sensors are a prerequisite for acquiring the environmental information for delivering to an artificial data center to make decisions. The MXene-based sensors have aroused tremendous interest because of their extraordinary performances. In this review, the electrical, electronic, and optical properties of MXenes are first introduced. Next, the MXene-based sensors are discussed according to the sensing mechanisms such as electronic, electrochemical, and optical methods. Initially, biosensors are introduced based on chemiresistors and field-effect transistors. Besides, the wearable pressure sensor is demonstrated with piezoresistive devices. Third, the electrochemical methods include amperometry and electrochemiluminescence as examples. In addition, the optical approaches refer to surface plasmonic resonance and fluorescence resonance energy transfer. Moreover, the prospects are delivered of multimodal data fusion toward complicated human-like senses. Eventually, future opportunities for MXene research are conveyed in the new material discovery, structure design, and proof-of-concept devices.

Toward Smart Sensing by MXene.

In this work, our prime objective is to study the phenomena of quantum chaos and complexity in the machine learning dynamics of Quantum Neural Network (QNN). A Parameterized Quantum Circuits (PQCs) in the hybrid quantum-classical framework is introduced as a universal function approximator to perform optimization with Stochastic Gradient Descent (SGD). We employ a statistical and differential geometric approach to study the learning theory of QNN. The evolution of parametrized unitary operators is correlated with the trajectory of parameters in the Diffusion metric. We establish the parametrized version of Quantum Complexity and Quantum Chaos in terms of physically relevant quantities, which are not only essential in determining the stability, but also essential in providing a very significant lower bound to the generalization capability of QNN. We explicitly prove that when the system executes limit cycles or oscillations in the phase space, the generalization capability of QNN is maximized. Finally, we have determined the generalization capability bound on the variance of parameters of the QNN in a steady state condition using Cauchy Schwartz Inequality.

/pdf/chaos-and-complexity-from-quantum-neural-network-a-study-34audfbkd0.pdf

Chaos and Complexity from Quantum Neural Network: A study with Diffusion Metric in Machine Learning

Fully Stretchable, Porous Mxene-Graphene Foam Nanocomposites for Energy Harvesting and Self-Powered Sensing

/pdf/chaos-and-complexity-from-quantum-neural-network-a-study-458zrfx9yu.pdf

Although flexible humidity sensors are essential for human health monitoring, it is still challenging to achieve high sensitivity and easy disposal with simple, low-cost fabrication processes. This study presents the design and fabrication of highly reliable hand-drawn interdigital electrodes from pencil-on-paper treated with NaCl solution for highly sensitive hydration sensors working over a wide range of relative humidity (RH) levels from 5.6% to 90%. The applications of the resulting flexible humidity sensor go beyond the monitoring of respiratory rate and proximity to characterizations of human skin types and evaluations of skin barrier functions through insensible sweat measurements. The sensor array can also be integrated with a diaper to result in smart diapers to alert for an early diaper change. The design and fabrication strategies presented in this work could also be leveraged for the development of wearable, self-powered, and recyclable sensors and actuators in the future.

Pencil-on-Paper Humidity Sensor Treated with NaCl Solution for Health Monitoring and Skin Characterization.

Monitoring nitrogen utilization efficiency and soil temperature in agricultural systems for timely intervention is essential for crop health with reduced environmental pollution. Herein, this work presents a high‐performance multi‐parameter sensor based on vanadium oxide (VOX)‐doped laser‐induced graphene (LIG) foam to completely decouple nitrogen oxides (NOX) and temperature. The highly porous 3D VOX‐doped LIG foam composite is readily obtained by laser scribing vanadium sulfide (V5S8)‐doped block copolymer and phenolic resin self‐assembled films. The heterojunction formed at the LIG/VOX interface provides the sensor with enhanced response to NOX and an ultralow limit of detection of 3 ppb (theoretical estimate of 451 ppt) at room temperature. The sensor also exhibits a wide detection range, fast response/recovery, good selectivity, and stability over 16 days. Meanwhile, the sensor can accurately detect temperature over a wide linear range of 10–110 °C. The encapsulation of the sensor with a soft membrane further allows for temperature sensing without being affected by NOX. The unencapsulated sensor operated at elevated temperature removes the influences of relative humidity and temperature variations for accurate NOX measurements. The capability to decouple nitrogen loss and soil temperature paves the way for the development of future multimodal decoupled electronics for precision agriculture and health monitoring.

/pdf/vanadium-oxide-doped-laser-induced-graphene-multi-parameter-3mr5bddo.pdf

Ankan Dutta

Papers

Chaos and Complexity from Quantum Neural Network: A study with Diffusion Metric in Machine Learning

Fully Stretchable, Porous Mxene-Graphene Foam Nanocomposites for Energy Harvesting and Self-Powered Sensing

Chaos and Complexity from Quantum Neural Network: A study with Diffusion Metric in Machine Learning

Pencil-on-Paper Humidity Sensor Treated with NaCl Solution for Health Monitoring and Skin Characterization.

Vanadium Oxide‐Doped Laser‐Induced Graphene Multi‐Parameter Sensor to Decouple Soil Nitrogen Loss and Temperature