arXiv subjects

Chandan Jana

Publications and source records attributed to Chandan Jana.

8 recordsLinked to original sources

arXiv2022

Operator Complexity for Quantum Scalar Fields and Cosmological Perturbations

We calculate the operator complexity for the displacement, squeeze and rotation operators of a quantum harmonic oscillator. The complexity of the time-dependent displacement operator is constant, equal to the magnitude of the coherent state parameter, while the complexity of unitary evolution by a generic quadratic Hamiltonian is proportional to the amount of squeezing and is sensitive to the time-dependent phase of the unitary operator. We apply these results to study the complexity of a free massive scalar field, finding that the complexity has a period of rapid linear growth followed by a saturation determined by the UV cutoff and the number of spatial dimensions. We also study the complexity of the unitary evolution of quantum cosmological perturbations in de Sitter space, which can be written as time-dependent squeezing and rotation operators on individual Fourier mode pairs. The complexity of a single mode pair at late times grows linearly with the number of e-folds, while the complexity at early times oscillates rapidly due to the sensitivity of operator complexity to the phase of unitary time evolution. Integrating over all modes, the total complexity of cosmological perturbations scales as the square root of the (exponentially) growing volume of de Sitter space, suggesting that inflation leads to an explosive growth in complexity of the Universe.

hep-th↗

arXiv2022

A study of non-linear Langevin dynamics under non-Gaussian noise with quartic cumulant

We consider a non-linear Langevin equation in presence of non-Gaussian noise originating from non-linear bath. We claim, the parameters in the Langevin equation are not physical. The physical parameters are obtained from a path-integral description of the system, where the Langevin parameters are related to the physical parameters by renormalisation flow equations. Then we compute both numerically and analytically the velocity two point function and show that it saturates to the bath temperature even in presence of non-linearity. We also find the velocity four point function numerically and show that it saturates to the analytically evaluated thermal velocity four point function when the non-linear FDR [1] is satisfied. When the non-linear FDR, which is a manifestation of time reversibility of thermal bath, is violated then the system does not seem to thermalise. Rather, its velocity four point function settles to a steady state.

cond-mat.stat-mech↗

arXiv2021

Saturation of Thermal Complexity of Purification

We purify the thermal density matrix of a free harmonic oscillator as a two-mode squeezed state, characterized by a squeezing parameter and squeezing angle. While the squeezing parameter is fixed by the temperature and frequency of the oscillator, the squeezing angle is otherwise undetermined, so that the complexity of purification is obtained by minimizing the complexity of the squeezed state over the squeezing angle. The resulting complexity of the thermal state is minimized at non-zero values of the squeezing angle and saturates to an order one number at high temperatures, indicating that there is no additional operator cost required to build thermal states beyond a certain temperature. We also review applications in which thermal density matrices arise for quantum fields on curved spacetimes, including Hawking radiation and a simple model of decoherence of cosmological density perturbations in the early Universe. The complexity of purification for these mixed states also saturates as a function of the effective temperature, which may have interesting consequences for the quantum information stored in these systems.

hep-th↗

arXiv2020

Open quantum systems and Schwinger-Keldysh holograms

We initiate the study of open quantum field theories using holographic methods. Specifically, we consider a quantum field theory (the system) coupled to a holographic field theory at finite temperature (the environment). We investigate the effects of integrating out the holographic environment with an aim of obtaining an effective dynamics for the resulting open quantum field theory. The influence functionals which enter this open effective action are determined by the real-time (Schwinger-Keldysh) correlation functions of the holographic thermal environment. To evaluate the latter, we exploit recent developments, wherein the semiclassical gravitational Schwinger-Keldysh saddle geometries were identified as complexified black hole spacetimes. We compute real-time correlation functions using holographic methods in these geometries, and argue that they lead to a sensible open effective quantum dynamics for the system in question, a question that hitherto had been left unanswered. In addition to shedding light on open quantum systems coupled to strongly correlated thermal environments, our results also provide a principled computation of Schwinger-Keldysh observables in gravity and holography. In particular, these influence functionals we compute capture both the dissipative physics of black hole quasinormal modes, as well as that of the fluctuations encoded in outgoing Hawking quanta, and interactions between them. We obtain results for these observables at leading order in a low frequency and momentum expansion in general dimensions, in addition to determining explicit results for two dimensional holographic CFT environments.

hep-th↗

arXiv2020

Nonlinear Langevin dynamics via holography

In this work, we consider non-linear corrections to the Langevin effective theory of a heavy quark moving through a strongly coupled CFT plasma. In AdS/CFT, this system can be identified with that of a string stretched between the boundary and the horizon of an asymptotically AdS black-brane solution. We compute the Feynman-Vernon influence phase for the heavy quark by evaluating the Nambu-Goto action on a doubled string configuration. This configuration is the linearised solution of the string motion in the doubled black-brane geometry which has been proposed as the holographic dual of a thermal Schwinger-Keldysh contour of the CFT. Our expression for the influence phase passes non-trivial consistency conditions arising from the underlying unitarity and thermality of the bath. The local effective theory obeys the recently proposed non-linear fluctuation dissipation theorem relating the non-Gaussianity of thermal noise to the thermal jitter in the damping constant. This furnishes a non-trivial check for the validity of these relations derived in the weak coupling regime.

hep-th↗

arXiv2019

Renormalisation in Open Quantum Field theory II: Yukawa theory and PV reduction

We compute Passarino-Veltman (PV) reduction for tensor loop integrals, that appear in open field theories. We apply these results to open-Yukawa theory and compute the self-energy correction of the fields. We found that non-local divergences show up in the one loop correction to the fermionic self-energy. These non-local divergences do not disappear even if the tree level theory is chosen to satisfy the trace preserving condition of the density matrix.

hep-th↗

arXiv2017

Renormalization in Open Quantum Field theory I: Scalar field theory

While the notion of open quantum systems is itself old, most of the existing studies deal with quantum mechanical systems rather than quantum field theories. After a brief review of field theoretical/path integral tools currently available to deal with open quantum field theories, we go on to apply these tools to an open version of $ϕ^3$ + $ϕ^4$ theory in four spacetime dimensions and demonstrate its one loop renormalizability (including the renormalizability of the Lindblad structure).

hep-th↗

arXiv2006

Structure of poly(propyl ether imine) (PETIM) dendrimer from fully atomistic molecular Dynamics Simulation and by Small Angle X-ray scattering

We study the structure of carboxylic acid terminated neutral poly (propyl ether imine) (PETIM) dendrimer from generation 1 through 6 (G1-G6) in a good solvent (water) by fully atomistic molecular dynamics (MD) simulations. We determine as a function of generation such structural properties as: radius of gyration, shape tensor, asphericity, fractal dimension, monomer density distribution, and end-group distribution functions. The sizes obtained from the MD simulations have been validated by Small Angle X-Ray Scattering (SAXS) experiment on dendrimer of generation 2 to 4 (G2-G4). A good agreement between the experimental and theoretical value of radius of gyration has been observed. We find a linear increase in radius of gyration with the generation. In contrast, Rg scales as ~ N^x with the number of monomers. We find two distinct exponents depending on the generations: x = 0.47 for G1-G3 and x = 0.28 for G3-G6 which reveals their non-space filling nature. In comparison with the amine terminated PAMAM dendrimer, we find Rg of G-th generation PETIM dendrimer is nearly equal to that of (G+1)-th generation of PAMAM dendrimer as observed by Maiti et. al. [Macromolecules,38, 979 2005]. We find substantial back folding of the outer sub generations into the interior of the dendrimer. Due to their highly flexible nature of the repeating branch units, the shape of the PETIM dendrimer deviates significantly from the spherical shape and the molecules become more and more spherical as the generation increases. The interior of the dendrimer is quite open with internal cavities available for accommodating guest molecules suggesting using PETIM dendrimer for guest-host applications. We also give a quantitative measure of the number of water molecules present inside the dendrimer.

cond-mat.soft↗