Kinjalk Lochan

Tata Institute of Fundamental Research, Mumbai, Maharashtra, India

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Publications (19)86.99 Total impact

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    Satyabrata Sahu, Kinjalk Lochan, D. Narasimha
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    ABSTRACT: We study gravitational lensing by a recently proposed black hole solution in Loop Quantum Gravity. We highlight the fact that the quantum gravity corrections to the Schwarzschild metric in this model evade the `mass suppression' effects (that the usual quantum gravity corrections are susceptible to) by virtue of one of the parameters in the model being dimensionless, which is unlike any other quantum gravity motivated parameter. Gravitational lensing in the strong and weak deflection regimes is studied and a sample consistency relation is presented which could serve as a test of this model. We discuss that though the consistency relation for this model is qualitatively similar to what would have been in Brans-Dicke, in general it can be a good discriminator between many alternative theories. Although the observational prospects do not seem to be very optimistic even for a galactic supermassive black hole case, time delay between relativistic images for billion solar mass black holes in other galaxies might be within reach of future relativistic lensing observations.
    Physical Review D 02/2015; 91(6). DOI:10.1103/PhysRevD.91.063001
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    ABSTRACT: Can certain degrees of freedom of a closed physical system, described by a time-independent Hamiltonian, become more and more classical as they evolve from 1 some state? This question is important because our universe seems to have done just that! We construct an explicit, simple, example of such a system with just two degrees of freedom, of which one achieves `spontaneous classicalization'. It starts from a quantum state and under the usual Hamiltonian evolution, becomes more and more classical (in a well-defined manner in terms of the Wigner function) as time progresses. This is achieved without the usual procedures of integrating out a large number of environmental degrees of freedom or conventional decoherence. We consider different ranges of parameter space and identify the conditions under which spontaneous classicalization occurs in our model. The mutual interaction between the sub-systems of a larger system can indeed drive some of the subsystems to a classical configuration, with a phase space trajectory of evolution. We also argue that the results of our toy model may well be general characteristics of certain class of interacting systems. Several implications are discussed.
    General Relativity and Gravitation 12/2014; 47(1). DOI:10.1007/s10714-014-1841-9
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    Kinjalk Lochan, T. Padmanabhan
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    ABSTRACT: The appearance of the inertial vacuum state in Rindler frame has been extensively studied in the literature, both from the point of view of QFT developed using Rindler foliation and using the response of an Unruh-Dewitt Detector (UDD). In comparison, less attention has been devoted to the study of inertial non-vacuum states when viewed from the Rindler frame. We provide a comprehensive study of this issue in this paper. We first present a general formalism describing characterization of an arbitrary inertial state when described using (i) an arbitrary foliation and (ii) the response of UDD moving along an arbitrary trajectory. We use this formalism to explicitly compute the results for the Rindler frame and uniformly accelerated detectors. Any arbitrary inertial state will always have a thermal component in the Rindler frame with additional contributions arising from the non-vacuum nature of the inertial state. We classify the nature of the additional contributions in terms of functions characterizing the inertial state. We establish that for all physically well behaved normalizable inertial states, the correction terms decay with the energy of the Rindler mode so that the high frequency limit is dominated by the thermal noise. However, inertial states which are not strictly normalizable, lead to a constant contribution at all high frequencies in the Rindler frame. A similar behavior arises in the response of the UDD as well. In the case of the detector response, we provide a physical interpretation for the constant contribution at high frequencies in terms of total detection rate of co-moving inertial detectors. We discuss two different approaches for defining a transition rate for the UDD, when the two-point function lacks the time translation invariance and discuss several features of different definitions of transition rates. The implications are discussed.
    Physical Review D 11/2014; 91(4). DOI:10.1103/PhysRevD.91.044002
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    ABSTRACT: It has been suggested in the literature that spatial coherence of the wave function can be dynamically suppressed by fluctuations in the gravity of spacetime. These fluctuations represent the minimal uncertainty that is present when one probes spacetime geometry with a quantum probe. Two similar models have been proposed, one by Di\'osi [D-model] and one by Karolyhazy and collaborators [K-model], based on apparently unrelated minimal spacetime bounds. The two models arrive at somewhat different expressions for the dependence of the localization coherence length on the mass and size of the quantum object. In the present article we compare and contrast the two models. We show that under certain conditions the minimal spacetime bounds in the two models can be derived one from the other. We also derive the two-point correlation for the fluctuation potential in the K-model, and show that it is non-white noise, unlike in the D-model, where the corresponding correlation is white noise in time. This seems to be the origin of the different results in the two models. We derive the non-Markovian master equation for the K-model. We argue that the minimal spacetime bound cannot predict the noise correlation uniquely, and additional criteria are necessary to accurately determine the effects of gravitationally induced decoherence.
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    ABSTRACT: Can certain degrees of freedom of a closed physical system, described by a time-independent Hamiltonian, become more and more classical as they evolve from some state? This question is important because our universe seems to have done just that! We construct an explicit, simple, example of such a system with just two degrees of freedom, of which one achieves `spontaneous classicalization'. It starts from a quantum state and under the usual Hamiltonian evolution, becomes more and more classical (in a well-defined manner in terms of the Wigner function) as time progresses. This is achieved without the usual procedures of integrating out a large number of environmental degrees of freedom or conventional decoherence. We consider different ranges of parameter space and identify the conditions under which spontaneous classicalization occurs in our model. The mutual interaction between the sub-systems of a larger system can indeed drive some of the subsystems to a classical configuration, with a phase space trajectory of evolution. We also argue that the results of our toy model may well be general characteristics of certain class of interacting systems. Several implications are discussed.
  • K Lochan, T P Singh
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    ABSTRACT: Trace Dynamics is a classical theory of non-commuting matrices, which uses cyclic permutation inside a trace to define the derivative with respect to an operator. We have used the methods of Trace Dynamics to construct a non-commutative special relativity. We have defined a line-element using the trace over spacetime coordinates, which are assumed to be operators. The line-element is shown to be invariant under generalized Lorentz transformations, and is used to construct a non-commutative relativistic dynamics. We have been motivated for such an operator structure at a more fundamental level, and attempt to obtain an emergent picture of classical spacetime.
    Journal of Physics Conference Series 03/2014; 484(1):012065. DOI:10.1088/1742-6596/484/1/012065
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    ABSTRACT: The inflationary paradigm provides a mechanism to generate the primordial perturbations needed to explain the observed large scale structures in the universe. Inflation traces back all the inhomogeneities to quantum fluctuations although the structures look classical today. Squeezing of primordial quantum fluctuations along with the mechanism of decoherence accounts for many aspects of this quantum to classical transition, although it remains a matter of debate as to whether this is sufficient to explain the issue of realization of a single outcome (i.e. the issue of macro-objectification) from a quantum ensemble given that the universe is a closed system. A similar question of emergence of classical behavior of macroscopic objects exists also for laboratory systems and apart from decoherence there have been attempts to resolve this issue through Continuous Spontaneous Localization (CSL), which is a stochastic nonlinear modification of the non-relativistic Schr\"{o}dinger equation. Recently, Martin {\it et al.} have investigated whether a CSL-like mechanism with a constant strength parameter, when the Mukhanov-Sasaki variable is taken as the "collapse-operator", can explain how the primordial quantum perturbations generated during inflation become classical. Within the scope of their assumptions they essentially come to a negative conclusion. In the present work, we generalize their analysis by allowing the CSL strength parameter to depend on physical scales so as to capture the CSL amplification mechanism. We show that such a generalization provides a mechanism for macro-objectification (i.e. classicalization) of the inflationary quantum perturbations, while also preserving scale invariance of the power spectrum and phase coherence of super-horizon perturbation modes in a particular class of these models.
    Physical review D: Particles and fields 04/2013; 88(8). DOI:10.1103/PhysRevD.88.085020
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    Suratna Das, Kinjalk Lochan, Angelo Bassi
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    ABSTRACT: Continuous Spontaneous Localization (CSL) model of Quantum Mechanics modifies Schr\"{o}dinger equation by adding non-linear stochastic terms due to which the total energy of a system increases with a constant rate which is proportional to the collapse rate $\lambda$. Thus applying CSL model to cosmological scenarios can change the thermal behaviour of the particles during evolution and we will put constraints on $\lambda$ by considering several cosmological scenarios.
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    ABSTRACT: This brief article reviews stochastic processes as relevant to dynamical models of wave-function collapse, and is supplemental material for the review article arXiv:1204.4325
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    Seema Satin, Kinjalk Lochan, Sukratu Barve
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    ABSTRACT: We attempt to calculate the point separated Noise Kernel for self similar Tolman Bondi metric, using a method similar to that developed by Eftekharzadeh et. al for ultra-static spacetimes referring to the work by Page. In case of formation of a naked singularity, the Noise Kernel thus obtained is found to be regular except on the Cauchy horizon, where it diverges. The behavior of the noise in case of the formation of a covered singularity is found to be regular. This result seemingly renders back reaction non-negligible which questions the stability of the results obtained from the semiclassical treatment of the self similar Tolman Bondi metric.
    Physical review D: Particles and fields 10/2012; 87(8). DOI:10.1103/PhysRevD.87.084067
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    Kinjalk Lochan, Suratna Das, Angelo Bassi
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    ABSTRACT: Models of spontaneous wave function collapse modify the linear Schrödinger equation of standard quantum mechanics by adding stochastic nonlinear terms to it. The aim of such models is to describe the quantum (linear) nature of microsystems along with the classical nature (violation of superposition principle) of macroscopic ones. The addition of such nonlinear terms in the Schrödinger equation leads to nonconservation of energy of the system under consideration. Thus, a striking feature of collapse models is to heat nonrelativistic particles with a constant rate. If such a process is physical, then it has the ability to perturb the well-understood thermal history of the universe. In this article we will try to investigate the impacts of such heating terms, according to the continuous spontaneous localization model, on the standard evolution of nonrelativistic matter and on the formation of cosmic microwave background radiation. We will also put constraints on the continuous spontaneous localization collapse rate λ by considering that the standard evolution of nonrelativistic matter is not hampered and the observed precise blackbody spectrum of cosmic microwave background radiation would not get distorted (in the form of μ-type and y-type distortions) so as to violate the observed bounds.
    Physical review D: Particles and fields 09/2012; 86(6). DOI:10.1103/PhysRevD.86.065016
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    Kinjalk Lochan, Cenalo Vaz
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    ABSTRACT: In this paper we discuss the entropy of quantum black holes in the LQG formalism when the number of punctures on the horizon is treated as a quantum hair, that is we compute the black hole entropy in the grand canonical (area) ensemble. The entropy is a function of both the average area and the average number of punctures and bears little resemblance to the Bekenstein-Hawking entropy. In the thermodynamic limit, both the "temperature" and the chemical potential can be shown to be functions only of the average area per puncture. At a fixed temperature, the average number of punctures becomes proportional to the average area and we recover the Bekenstein-Hawking area-entropy law to leading order provided that the Barbero-Immirzi parameter, $\gamma$, is appropriately fixed. This also relates the chemical potential to $\gamma$. We obtain a sub-leading correction, which differs in signature from that obtained in the microcanonical and canonical ensembles in its sign but agrees with earlier results in the grand canonical ensemble.
    Physical review D: Particles and fields 05/2012; 86(4). DOI:10.1103/PhysRevD.86.044035
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    Cenalo Vaz, Kinjalk Lochan
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    ABSTRACT: We extend previous results on the reflection and transmission of self-gravitating dust shells across the apparent horizon during quantum dust collapse to non-marginally-bound dust collapse in arbitrary dimensions with a negative cosmological constant. We show that the Hawking temperature is independent of the energy function and that the wave functional describing the collapse is well behaved at the Hawking-Page transition point. Thermal radiation from the apparent horizon appears as a generic result of non-marginal collapse in AdS space-time owing to the singular structure of the Hamiltonian constraint at the apparent horizon.
    Physical review D: Particles and fields 04/2012; 87(2). DOI:10.1103/PhysRevD.87.024045
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    ABSTRACT: Quantum mechanics is an extremely successful theory that agrees with every experiment. However, the principle of linear superposition, a central tenet of the theory, apparently contradicts a commonplace observation: macroscopic objects are never found in a linear superposition of position states. Moreover, the theory does not really explain as to why during a quantum measurement, deterministic evolution is replaced by probabilistic evolution, whose random outcomes obey the Born probability rule. In this article we review an experimentally falsifiable phenomenological proposal, known as Continuous Spontaneous Collapse: a stochastic non-linear modification of the Schr\"{o}dinger equation, which resolves these problems, while giving the same experimental results as quantum theory in the microscopic regime. Two underlying theories for this phenomenology are reviewed: Trace Dynamics, and gravity induced collapse. As one approaches the macroscopic scale, the predictions of this proposal begin to differ appreciably from those of quantum theory, and are being confronted by ongoing laboratory experiments that include molecular interferometry and optomechanics. These experiments, which essentially test the validity of linear superposition for large systems, are reviewed here, and their technical challenges, current results, and future prospects summarized. We conclude that it is likely that over the next two decades or so, these experiments can verify or rule out the proposed stochastic modification of quantum theory.
    Review of Modern Physics 04/2012; 85(2). DOI:10.1103/RevModPhys.85.471
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    Kinjalk Lochan, Seema Satin, Tejinder P. Singh
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    ABSTRACT: There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter degrees of freedom are treated as classical matrices with arbitrary commutation relations, and a space-time line element is defined using a trace. In the present paper, following the theory of Trace Dynamics, we construct a statistical thermodynamics for the non-commutative special relativity, and show that one arrives at a generalized quantum dynamics in which space and time are non-classical and have an operator status. In a future work, we will show how standard quantum theory on a classical space-time background is recovered from here.
    Foundations of Physics 03/2012; 42(12). DOI:10.1007/s10701-012-9683-3
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    Kinjalk Lochan, Cenalo Vaz
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    ABSTRACT: We compute the canonical partition for quantum black holes in the approach of Loop Quantum Gravity (LQG). We argue that any quantum theory of gravity in which the horizon area is built of non-interacting constituents cannot yield qualitative corrections to the Bekenstein-Hawking (B-H) area law, but corrections to the area law can arise as a consequence additional constraints inducing interactions between the constituents. In LQG this is implemented by requiring spherical horizons. The canonical approach for LQG favours a logarithmic correction to the B-H law with a coefficient of -1/2, independently of the area spectrum. Our initial calculation of the partition function uses certain approximations that, we show, do not qualitatively affect the expression for the black hole entropy. We later discuss the quantitative corrections to these results when the simplifying approximations are relaxed and the full LQG spectrum is dealt with. We show how these corrections can be recovered to all orders in perturbation theory. However, the convergence properties of the perturbative series remains unknown.
    Physical review D: Particles and fields 02/2012; 85(10). DOI:10.1103/PhysRevD.85.104041
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    Kinjalk Lochan, T. P. Singh
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    ABSTRACT: Trace Dynamics is a classical dynamical theory of noncommuting matrices in which cyclic permutation inside a trace is used to define the derivative with respect to an operator. We use the methods of Trace Dynamics to construct a noncommutative special relativity. We define a line-element using the Trace over spacetime coordinates which are assumed to be operators. The line-element is shown to be invariant under standard Lorentz transformations, and is used to construct a noncommutative relativistic dynamics. The eventual motivation for constructing such a noncommutative relativity is to relate the statistical thermodynamics of this classical theory to quantum mechanics.
    Physics Letters A 10/2011; 375(43):3747-3750. DOI:10.1016/j.physleta.2011.09.003
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    ABSTRACT: We investigate a possible way of establishing a parallel between the third law of black hole mechanics, and the strong version of the third law of thermodynamics. We calculate the surface gravity and area for a naked singular null surface in the Gamma-metric and explain in what sense this behaviour violates thermodynamics.
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    Kinjalk Lochan, T. P. Singh
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    ABSTRACT: There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than about a thousand atoms. Secondly, there is no universally agreed upon explanation for the process of quantum measurement. Thirdly, there is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of position eigenstates. Fourthly, and perhaps most importantly, the concept of time is classical and hence external to quantum mechanics : there should exist an equivalent reformulation of the theory which does not refer to an external classical time. In this paper we argue that such a reformulation is the limiting case of a nonlinear quantum theory, with the nonlinearity becoming important at the Planck mass scale. Such a nonlinearity can provide insights into the problems mentioned above. We use a physically motivated model for a nonlinear Schrodinger equation to show that nonlinearity can help in understanding quantum measurement. We also show that while the principle of linear superposition holds to a very high accuracy for atomic systems, the lifetime of a quantum superposition becomes progressively smaller, as one goes from microscopic to macroscopic objects. This can explain the observed absence of position superpositions in macroscopic objects [lifetime is too small]. It also suggests that ongoing laboratory experiments maybe able to detect the finite superposition lifetime for mesoscopic objects, in the foreseeable future. Comment: Minor revision in Introduction. 23 pages. To appear in Pramana J. Phys
    Pramana 12/2009; 76(1). DOI:10.1007/s12043-011-0015-5