Causality in Discrete Time Physics Derived from Maupertuis Reduced Action Principle

Causality describes the process and consequences from an action: a cause has an effect. Causality is preserved in classical physics as well as in special and general theories of relativity. Surprisingly, causality as a relationship between the cause and its effect is in neither of these theories considered a law or a principle. Its existence in physics has even been challenged by prominent opponents in part due to the time symmetric nature of the physical laws. With the use of the reduced action and the least action principle of Maupertuis along with a discrete dynamical time physics yielding an arrow of time, causality is defined as the partial spatial derivative of the reduced action and as such is position- and momentum-dependent and requests the presence of space. With this definition the system evolves from one step to the next without the need of time, while (discrete) time can be reconstructed.

Estimation of temperature of cosmological apparent horizons: a new approach

We consider radiation from cosmological apparent horizon in Friedmann–Lemaitre–Robertson–Walker (FLRW) model in a double-null coordinate setting. As the spacetime is dynamic, there is no timelike Killing vector, instead we have Kodama vector which acts as dynamical time. We construct the positive frequency modes of the Kodama vector across the horizon. The conditional probability that a signal reaches the central observer when it is crossing from the outside gives the temperature associated with the horizon.

Customized depolarization spatial patterns with dynamic retardance functions

In this work we demonstrate customized depolarization spatial patterns by imaging a dynamical time-dependent pixelated retarder. A proof-of-concept of the proposed method is presented, where a liquid–crystal spatial light modulator is used as a spatial retarder that emulates a controlled spatially variant depolarizing sample by addressing a time-dependent phase pattern. We apply an imaging Mueller polarimetric system based on a polarization camera to verify the effective depolarization effect. Experimental validation is provided by temporal integration on the detection system. The effective depolarizance results are fully described within a simple graphical approach which agrees with standard Mueller matrix decomposition methods. The potential of the method is discussed by means of three practical cases, which include non-reported depolarization spatial patterns, including exotic structures as a spirally shaped depolarization pattern.

The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations

The underlying physical concept of computing out-of-time-ordered correlation (OTOC) is a significant new tool within the framework of quantum field theory, which now-a-days is treated as a measure of random fluctuations. In this paper, by following the canonical quantization technique, we demonstrate a computational method to quantify the two different types of cosmological auto-correlated OTO functions during the epoch when the non-equilibrium features dominates in primordial cosmology. In this formulation, two distinct dynamical time scales are involved to define the quantum mechanical operators arising from the cosmological perturbation scenario. We have provided detailed explanation regarding the necessity of this new formalism to quantify any random events generated from quantum fluctuations in primordial cosmology. We have performed an elaborative computation for the two types of two-point and four-point auto-correlated OTO functions in terms of the cosmological perturbation field variables and its canonically conjugate momenta to quantify random auto-correlations in the non-equilibrium regime. For both of the cases, we found significantly distinguishable non-chaotic, but random, behaviour in the OTO auto-correlations, which was not pointed out before in this type of study. Finally, we have also demonstrated the classical limiting behaviour of the mentioned two types of auto-correlated OTOC functions from the thermally weighted phase-space averaged Poisson brackets, which we found to exactly match the large time limiting behaviour of the auto-correlations in the super-horizon regime of the cosmological scalar mode fluctuation.

Bowen–York model solution redux

Initial value problem in general relativity is often solved numerically; with only a few exceptions one of which is the “model” solution of Bowen and York where an analytical form of the solution is available. The solution describes a dynamical, time-asymmetric, gravitating system with mass and linear momentum. Here we revisit this solution and correct an error which turns out to be important for identifying the energy-content of the solution. Depending on the linear momentum, the ratio of the non-stationary part of the initial energy to the total ADM energy takes values between [0, 0.592). This non-stationary part is expected to be turned into gravitational waves during the evolution of the system to possibly settle down to a black hole with mass and linear momentum. In the ultra-relativistic case (the high momentum limit), the maximum amount of gravitational wave energy is 59.2% of the total ADM energy. We also give a detailed account of the general solution of the Hamiltonian constraint.

The Cosmological OTOC: A New Proposal for Quantifying Auto-correlated Random Non-chaotic Primordial Fluctuations

The underlying physical concept of computing out-of-time-ordered correlation (OTOC) is a significant new tool within the framework of quantum field theory, which now-a-days is treated as a measure of random fluctuations. In this paper, by following the canonical quantization technique we demonstrate a computational method to quantify the two different types of Cosmological auto-correlated OTO functions during the epoch when the non-equilibrium features dominates in Primordial Cosmology. In this formulation, two distinct dynamical time scales are involved to define the quantum mechanical operators arising from cosmological perturbation scenario. We have provided detailed explanation regarding the necessity of this new formalism to quantify any random events generated from quantum fluctuations in Primordial Cosmology. We have performed an elaborative computation for the two types of two-point and four-point auto-correlated OTO functions in terms of the cosmological perturbation field variables and its canonically conjugate momenta to quantify random auto-correlations in the non-equilibrium regime. For both the cases we found significantly distinguishable non-chaotic, but random behaviour in the OTO auto-correlations, which was not pointed before in this type of studies. Finally, we have also demonstrated the classical limiting behaviour of the mentioned two types of auto-correlated OTOC functions from the thermally weighted phase space averaged Poisson Brackets, which we found exactly matches with the large time limiting behaviour of the auto-correlations in the super-horizon regime of the cosmological scalar mode fluctuation.

Customized Depolarization Spatial Patterns With Dynamic Retardance Functions

In this work we demonstrate customized depolarization spatial patterns by imaging a dynamical time-dependent pixelated retarder. A proof-of-concept of the proposed method is presented, where a liquid-crystal spatial light modulator is used as a spatial retarder that emulates a controlled spatially variant depolarizing sample by addressing a time-dependent phase mask. We apply an imaging Mueller polarimetric system based on a polarization camera to verify the effective depolarization effect. Experimental validation is provided by temporal integration on the detection system. The effective depolarizance results are fully described within a simple graphical approach which agrees with standard Mueller matrix decomposition methods. The potential of the method is discussed by means of three practical cases, which include non-reported depolarization spatial patterns, including exotic structures as a spirally shaped depolarization pattern.

The Cosmological OTOC: A New Proposal for Quantifying Auto-correlated Random Non-chaotic Primordial Fluctuations

The underlying physical concept of computing out-of-time-ordered correlation (OTOC) is a significant new tool within the framework of quantum field theory, which now-a-days is treated as a measure of random fluctuations. In this paper, by following the canonical quantization technique we demonstrate a computational method to quantify the two different types of Cosmological auto-correlated OTO functions during the epoch when the non-equilibrium features dominates in Primordial Cosmology. In this formulation, two distinct dynamical time scales are involved to define the quantum mechanical operators arising from cosmological perturbation scenario. We have provided detailed explanation regarding the necessity of this new formalism to quantify any random events generated from quantum fluctuations in Primordial Cosmology. We have performed an elaborative computation for the two types of two-point and four-point auto-correlated OTO functions in terms of the cosmological perturbation field variables and its canonically conjugate momenta to quantify random auto-correlations in the non-equilibrium regime. For both the cases we found significantly distinguishable non-chaotic, but random behaviour in the OTO auto-correlations, which was not pointed before in this type of studies. Finally, we have also demonstrated the classical limiting behaviour of the mentioned two types of auto-correlated OTOC functions from the thermally weighted phase space averaged Poisson Brackets, which we found exactly matches with the large time limiting behaviour of the auto-correlations in the super-horizon regime of the cosmological scalar mode fluctuation.

Dynamical time scales of friction dynamics in active microrheology of a model glass

Owing to the local/heterogeneous structures in supercooled liquids, after several decades of research, it is now clear that supercooled liquids are structurally different from their conventional liquid counterparts. Accordingly, an...