Wigner Function and Entanglement Entropy for Bosons from Non-Equilibrium Field Theory

We propose a new method of calculating entanglement entropy of a many-body interacting Bosonic system (open or closed) in a field theoretic approach without replica methods. The Wigner function and Renyi entropy of a Bosonic system undergoing arbitrary non-equilibrium dynamics can be obtained from its Wigner characteristic function, which we identify with the Schwinger Keldysh partition function in presence of quantum sources turned on at the time of measurement. For non-interacting many body systems, starting from arbitrary density matrices, we provide exact analytic formulae for Wigner function and entanglement entropy in terms of the single particle Green's functions. For interacting systems, we relate the Wigner characteristic to the connected multi-particle correlators of the system. We use this formalism to study the evolution of an open quantum system from a Fock state with negative Wigner function and zero entropy, to a thermal state with positive Wigner function and finite entropy. The evolution of the Renyi entropy is non-monotonic in time for both Markovian and non-Markovian dynamics. The entropy is also found to be anti-correlated with negativity of the Wigner function of a $2$ -mode open quantum system.Comment: 5+7 Pages, 2+2 Figure

Controlling Collective Phenomena by Engineering the Quantum State of Force Carriers: The Case of Photon-Mediated Superconductivity and its Criticality

How are the scattering between the constituents of matter and the resulting collective phenomena affected by preparing the force carriers in different quantum states? This question has become experimentally relevant in a specific non-relativistic version of QED implemented within materials, where standard techniques of quantum optics are available for the preparation of desired quantum states of the carrier photon. We develop the necessary non-equilibrium approach for computing the vertex function and find that, in addition to the energy and momentum structure of the scattering, a further structure emerges which reflects the Hilbert-space distribution of the carrier quantum state. This emergent structure becomes non-trivial for non-Gaussian quantum states of the force carrier, and can dramatically affect interactions and collective phenomena. As a first application, we show that by preparing photons in pure Fock states one can enhance pair correlations, and even control the criticality and universality class of the superconducting phase transition by the choice of the number of photons. Our results also reveal that the thermal mixture of Fock states regularises the strong pair correlations present in each of its components, yielding the standard Bardeen-Cooper-Schrieffer criticality.Comment: 17 +2 pages, 6 figure

Long-range photon fluctuations enhance photon-mediated electron pairing and superconductivity

Recently, the possibility of inducing superconductivity for electrons in two dimensional materials has been proposed via cavity-mediated pairing. The cavity-mediated electron-electron interactions are long range, which has two main effects: firstly, within the standard BCS-type pairing mediated by adiabatic photons, the superconducting critical temperature depends polynomially on the coupling strength, instead of the exponential dependence characterizing the phonon-mediated pairing; secondly, as we show here, the effect of photon fluctuations is significantly enhanced. These mediate novel non-BCS-type pairing processes, via non-adiabatic photons, which are not sensitive to the electron occupation but rather to the electron dispersion and lifetime at the Fermi surface. Therefore, while the leading temperature dependence of BCS pairing comes from the smoothening of the Fermi-Dirac distribution, the temperature dependence of the fluctuation-induced pairing comes from the electron lifetime. For realistic parameters, also including cavity loss, this results into a critical temperature which can be more than one order of magnitude larger than the BCS prediction. Moreover, a finite average number photons (as can be achieved by incoherently pumping the cavity) adds to the fluctuations and leads to a further enhancement of the critical temperature.Comment: published versio

Renyi Entropy of Interacting Thermal Bosons in Large NN Approximation

Using a Wigner function based approach, we study the Renyi entropy of a subsystem $A$ of a system of Bosons interacting with a local repulsive potential. The full system is assumed to be in thermal equilibrium at a temperature $T$ and density $\rho$. For a ${\cal U}(N)$ symmetric model, we show that the Renyi entropy of the system in the large $N$ limit can be understood in terms of an effective non-interacting system with a spatially varying mean field potential, which has to be determined self consistently. The Renyi entropy is the sum of two terms: (a) Renyi entropy of this effective system and (b) the difference in thermal free energy between the effective system and the original translation invariant system, scaled by $T$. We determine the self consistent equation for this effective potential within a saddle point approximation. We use this formalism to look at one and two dimensional Bose gases on a lattice. In both cases, the potential profile is that of a square well, taking one value in the subsystem $A$ and a different value outside it. The potential varies in space near the boundary of the subsystem $A$ on the scale of density-density correlation length. The effect of interaction on the entanglement entropy density is determined by the ratio of the potential barrier to the temperature and peaks at an intermediate temperature, while the high and low temperature regimes are dominated by the non-interacting answer.Comment: 12 pages, 4 figure

Charge and Entanglement Criticality in a U(1)-Symmetric Hybrid Circuit of Qubits

We study critical properties of the entanglement and charge-sharpening measurement-induced phase transitions in a non-unitary quantum circuit evolving with a U(1) conserved charge. Many critical properties appear distinct from the generic non-conserving case and percolation; however, upon interpreting the critical features as mixtures of both entanglement and charge-sharpening transitions, many critical features are brought within range of the generic case. Nonetheless, the multifractal properties of the entanglement transition remain distinct from the generic case without any symmetry, indicating a unique universality class due to the U(1) symmetry. We compute entanglement critical exponents and correlation functions via various ancilla measures, use a transfer matrix for multifractality, and compute correlators associated with charge sharpening to explain these findings. Through these correlators, we also find evidence consistent with the charge-sharpening transition being of the Berezinskii-Kosterlitz-Thouless type (including the predicted "jump" in stiffness), which simultaneously argues for a broad critical fan for this transition. As a result, attempts to measure critical properties in this system will see anomalously large exponents consistent with overlapping criticality.Comment: 12+5 pages, 8+6 figure

Boundary transfer matrix spectrum of measurement-induced transitions

Measurement-induced phase transitions (MIPTs) are known to be described by non-unitary conformal field theories (CFTs) whose precise nature remains unknown. Most physical quantities of interest, such as the entanglement features of quantum trajectories, are described by boundary observables in this CFT. We introduce a transfer matrix approach to study the boundary spectrum of this field theory, and consider a variety of boundary conditions. We apply this approach numerically to monitored Haar and Clifford circuits, and to the measurement-only Ising model where the boundary scaling dimensions can be derived analytically. Our transfer matrix approach provides a systematic numerical tool to study the spectrum of MIPTs.Comment: 17 pages, 12 figures, 1 tabl

Evaluation of antimicrobial activity of synthesized fluorocarbazole derivatives based on SAR

701-708The antimicrobial activity of synthesized 6-fluoro-1H-carbazole, 6-fluoro-2-methyl-1H-carbazole, 6-fluoro-3-methyl-1H-carbazole and their respective quinone derivatives 6-fluoro-1H-carbazole-1,4(9H)-dione, 6-fluoro-2-methyl-1H-carbazole-1,4(9H)-dione and 6-fluoro-3-methyl-1H-carbazole-1,4(9H)-dione have been studied against Escherichia coli (MTCC 42), Bacillus subtilis (MTCC 121), Staphylococcus aureus (MTCC 96), Methicillin-resistant Staphylococcus aureus (MRSA) and Pseudomonas sp. (MTCC 6199). The experimental results show that methylsubstituent at C-2 and C-3 along with electron withdrawing fluorine atom at C-6 in the carbazoloquinone as well as the corresponding carbazoles result in the remarkable antibacterial activity against MRSA. This finding is expected to fuel the existing structure-activity relationship for drug designing concept

Solid Phase Benzoylation of Phenols and Alcohols in Microwave Reactor: An Eco-Friendly Protocol

<div><p></p><p>An efficient solid phase benzoylation of phenols and alcohols was developed under microwave irradiation. Stoichiometric amount of benzoyl chloride was sufficient to carry out the reaction. This benzoylation features short reaction time, high yields and easy work-up procedures. Furthermore, the scope of the reaction was extended to prepare 3,5-dinitrobenzoyl derivatives of alcohols.</p></div