arXiv subjects

Aleksandar Bogojevic

Publications and source records attributed to Aleksandar Bogojevic.

At least 19 recordsLinked to original sources

arXiv2024

Terrestrial Very-Long-Baseline Atom Interferometry: Summary of the Second Workshop

This summary of the second Terrestrial Very-Long-Baseline Atom Interferometry (TVLBAI) Workshop provides a comprehensive overview of our meeting held in London in April 2024, building on the initial discussions during the inaugural workshop held at CERN in March 2023. Like the summary of the first workshop, this document records a critical milestone for the international atom interferometry community. It documents our concerted efforts to evaluate progress, address emerging challenges, and refine strategic directions for future large-scale atom interferometry projects. Our commitment to collaboration is manifested by the integration of diverse expertise and the coordination of international resources, all aimed at advancing the frontiers of atom interferometry physics and technology, as set out in a Memorandum of Understanding signed by over 50 institutions.

hep-ex↗

arXiv2023

Terrestrial Very-Long-Baseline Atom Interferometry: Workshop Summary

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions.

hep-ex↗

arXiv2022

CUDA programs for solving the time-dependent dipolar Gross-Pitaevskii equation in an anisotropic trap

In this paper we present new versions of previously published numerical programs for solving the dipolar Gross-Pitaevskii (GP) equation including the contact interaction in two and three spatial dimensions in imaginary and in real time, yielding both stationary and non-stationary solutions. New versions of programs were developed using CUDA toolkit and can make use of Nvidia GPU devices. The algorithm used is the same split-step semi-implicit Crank-Nicolson method as in the previous version (R. Kishor Kumar et al., Comput. Phys. Commun. 195, 117 (2015)), which is here implemented as a series of CUDA kernels that compute the solution on the GPU. In addition, the Fast Fourier Transform (FFT) library used in the previous version is replaced by cuFFT library, which works on CUDA-enabled GPUs. We present speedup test results obtained using new versions of programs and demonstrate an average speedup of 12 to 25, depending on the program and input size.

physics.comp-ph↗

arXiv2013

Scaling exponents and phase separation in a nonlinear network model inspired by the gravitational accretion

We study dynamics and scaling exponents in a nonlinear network model inspired by the formation of planetary systems. Dynamics of this model leads to phase separation to two types of condensate, light and heavy, distinguished by how they scale with mass. Light condensate distributions obey power laws given in terms of several identified scaling exponents that do not depend on initial conditions. The analyzed properties of heavy condensates have been found to be scale-free. Calculated mass distributions agree well with more complex models, and fit observations of both our own Solar System, and the best observed extra-solar planetary systems.

cond-mat.stat-mech↗

arXiv2011

SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach

We present Path Integral Monte Carlo C code for calculation of quantum mechanical transition amplitudes for 1D models. The SPEEDUP C code is based on the use of higher-order short-time effective actions and implemented to the maximal order $p$=18 in the time of propagation (Monte Carlo time step), which substantially improves the convergence of discretized amplitudes to their exact continuum values. Symbolic derivation of higher-order effective actions is implemented in SPEEDUP Mathematica codes, using the recursive Schroedinger equation approach. In addition to the general 1D quantum theory, developed Mathematica codes are capable of calculating effective actions for specific models, for general 2D and 3D potentials, as well as for a general many-body theory in arbitrary number of spatial dimensions.

cond-mat.stat-mech↗

arXiv2011

Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator

In this and subsequent paper arXiv:1011.5185 we develop a recursive approach for calculating the short-time expansion of the propagator for a general quantum system in a time-dependent potential to orders that have not yet been accessible before. To this end the propagator is expressed in terms of a discretized effective potential, for which we derive and analytically solve a set of efficient recursion relations. Such a discretized effective potential can be used to substantially speed up numerical Monte Carlo simulations for path integrals, or to set up various analytic approximation techniques to study properties of quantum systems in time-dependent potentials. The analytically derived results are numerically verified by treating several simple models.

cond-mat.stat-mech↗

arXiv2011

Fast Converging Path Integrals for Time-Dependent Potentials II: Generalization to Many-body Systems and Real-Time Formalism

Based on a previously developed recursive approach for calculating the short-time expansion of the propagator for systems with time-independent potentials and its time-dependent generalization for simple single-particle systems, in this paper we present a full extension of this formalism to a general quantum system with many degrees of freedom in a time-dependent potential. Furthermore, we also present a recursive approach for the velocity-independent part of the effective potential, which is necessary for calculating diagonal amplitudes and partition functions, as well as an extension from the imaginary-time formalism to the real-time one, which enables to study the dynamical properties of quantum systems. The recursive approach developed here allows an analytic derivation of the short-time expansion to orders that have not been accessible before, using the implemented SPEEDUP symbolic calculation code. The analytically derived results are extensively numerically verified by treating several models in both imaginary and real time.

cond-mat.stat-mech↗

arXiv2010

Ultra-Fast Converging Path-Integral Approach for Rotating Ideal Bose-Einstein Condensates

A recently developed efficient recursive approach for analytically calculating the short-time evolution of the one-particle propagator to extremely high orders is applied here for numerically studying the thermodynamical and dynamical properties of a rotating ideal Bose gas of $^{87}$Rb atoms in an anharmonic trap. At first, the one-particle energy spectrum of the system is obtained by diagonalizing the discretized short-time propagator. Using this, many-boson properties such as the condensation temperature, the ground-state occupancy, density profiles, and time-of-flight absorption pictures are calculated for varying rotation frequencies. The obtained results improve previous semiclassical calculations, in particular for smaller particle numbers. Furthermore, we find that typical time scales for a free expansion are increased by an order of magnitude for the delicate regime of both critical and overcritical rotation.

cond-mat.quant-gas↗

arXiv2009

Properties of Quantum Systems via Diagonalization of Transition Amplitudes I: Discretization Effects

We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors associated with space discretization. Approaches using direct diagonalization of real-space discretized Hamiltonians lead to polynomial errors in discretization spacing $Δ$. Here we show that the method based on the diagonalization of the short-time evolution operators leads to substantially smaller discretization errors, vanishing exponentially with $1/Δ^2$. As a result, the presented calculation scheme is particularly well suited for numerical studies of few-body quantum systems. The analytically derived discretization errors estimates are numerically shown to hold for several models. In the followup paper [1] we present and analyze substantial improvements that result from the merger of this approach with the recently introduced effective-action scheme for high-precision calculation of short-time propagation.

cond-mat.stat-mech↗

arXiv2009

Properties of Quantum Systems via Diagonalization of Transition Amplitudes II: Systematic Improvements of Short-time Propagation

In this paper, building on a previous analysis [1] of exact diagonalization of the space-discretized evolution operator for the study of properties of non-relativistic quantum systems, we present a substantial improvement to this method. We apply recently introduced effective action approach for obtaining short-time expansion of the propagator up to very high orders to calculate matrix elements of space-discretized evolution operator. This improves by many orders of magnitude previously used approximations for discretized matrix elements and allows us to numerically obtain large numbers of accurate energy eigenvalues and eigenstates using numerical diagonalization. We illustrate this approach on several one and two-dimensional models. The quality of numerically calculated higher order eigenstates is assessed by comparison with semiclassical cumulative density of states.

cond-mat.stat-mech↗

arXiv2008

Recursive Schr\" odinger Equation Approach to Faster Converging Path Integrals

By recursively solving the underlying Schr\" odinger equation, we set up an efficient systematic approach for deriving analytic expressions for discretized effective actions. With this we obtain discrete short-time propagators for both one and many particles in arbitrary dimension to orders which have not been accessible before. They can be used to substantially speed up numerical Monte Carlo calculations of path integrals, as well as for setting up a new analytical approximation scheme for energy spectra, density of states, and other statistical properties of quantum systems.

cond-mat.stat-mech↗

arXiv2008

Consequences of increased longevity for wealth, fertility, and population growth

We present, solve and numerically simulate a simple model that describes the consequences of increased longevity on fertility rates, population growth and the distribution of wealth in developed societies. We look at the consequences of the repeated use of life extension techniques and show that they represent a novel commodity whose introduction will profoundly influence key aspects of economy and society in general. In particular, we uncover two phases within our simplified model, labeled as 'mortal' and 'immortal'. Within the life extension scenario it is possible to have sustainable economic growth in a population of stable size, as a result of dynamical equilibrium between the two phases.

q-fin.GN↗

arXiv2008

Fast Convergence of Path Integrals for Many-body Systems

We generalize a recently developed method for accelerated Monte Carlo calculation of path integrals to the physically relevant case of generic many-body systems. This is done by developing an analytic procedure for constructing a hierarchy of effective actions leading to improvements in convergence of $N$-fold discretized many-body path integral expressions from 1/N to $1/N^p$ for generic $p$. In this paper we present explicit solutions within this hierarchy up to level $p=5$. Using this we calculate the low lying energy levels of a two particle model with quartic interactions for several values of coupling and demonstrate agreement with analytical results governing the increase in efficiency of the new method. The applicability of the developed scheme is further extended to the calculation of energy expectation values through the construction of associated energy estimators exhibiting the same speedup in convergence.

cond-mat.stat-mech↗

arXiv2006

Efficient Calculation of Energy Spectra Using Path Integrals

A newly developed method for systematically improving the convergence of path integrals for transition amplitudes, introduced in Phys. Rev. Lett. 94 (2005) 180403, Phys. Rev. B 72 (2005) 064302, Phys. Lett. A 344 (2005) 84, and expectation values, introduced in Phys. Lett. A 360 (2006) 217, is here applied to the efficient calculation of energy spectra. We show how the derived hierarchies of effective actions lead to substantial speedup of the standard path integral Monte Carlo evaluation of energy levels. The general results and the ensuing increase in efficiency of several orders of magnitude are shown using explicit Monte Carlo simulations of several distinct models.

cond-mat.stat-mech↗

arXiv2006

Energy Estimators and Calculation of Energy Expectation Values in the Path Integral Formalism

A recently developed method, introduced in Phys. Rev. Lett. 94 (2005) 180403, Phys. Rev. B 72 (2005) 064302, Phys. Lett. A 344 (2005) 84, systematically improved the convergence of generic path integrals for transition amplitudes. This was achieved by analytically constructing a hierarchy of $N$-fold discretized effective actions $S^{(p)}_N$ labeled by a whole number $p$ and starting at $p=1$ from the naively discretized action in the mid-point prescription. The derivation guaranteed that the level $p$ effective actions lead to discretized transition amplitudes differing from the continuum limit by a term of order $1/N^p$. Here we extend the applicability of the above method to the calculation of energy expectation values. This is done by constructing analytical expressions for energy estimators of a general theory for each level $p$. As a result of this energy expectation values converge to the continuum as $1/N^p$. Finally, we perform a series of Monte Carlo simulations of several models, show explicitly the derived increase in convergence, and the ensuing speedup in numerical calculation of energy expectation values of many orders of magnitude.

cond-mat.stat-mech↗

arXiv2005

Systematic Speedup of Path Integrals of a Generic $N$-fold Discretized Theory

We present and discuss a detailed derivation of a new analytical method that systematically improves the convergence of path integrals of a generic $N$-fold discretized theory. We develop an explicit procedure for calculating a set of effective actions $S^{(p)}$, for $p=1,2,3,...$ which have the property that they lead to the same continuum amplitudes as the starting action, but that converge to that continuum limit ever faster. Discretized amplitudes calculated using the $p$ level effective action differ from the continuum limit by a term of order $1/N^p$. We obtain explicit expressions for the effective actions for levels $p\le 9$. We end by analyzing the speedup of Monte Carlo simulations of two different models: an anharmonic oscillator with quartic coupling and a particle in a modified Pöschl-Teller potential.

cond-mat.stat-mech↗

arXiv2005

Asymptotic Properties of Path Integral Ideals

We introduce and analyze a new quantity, the path integral ideal, governing the flow of generic discrete theories to the continuum limit and greatly increasing their convergence. The said flow is classified according to the degree of divergence of the potential at spatial infinity. Studying the asymptotic behavior of path integral ideals we isolate the dominant terms in the effective potential that determine the behavior of a generic theory for large discrete time steps.

cond-mat.stat-mech↗

arXiv2005

Generalization of Euler's Summation Formula to Path Integrals

A recently developed analytical method for systematic improvement of the convergence of path integrals is used to derive a generalization of Euler's summation formula for path integrals. The first $p$ terms in this formula improve convergence of path integrals to the continuum limit from 1/N to $1/N^p$, where $N$ is the coarseness of the discretization. Monte Carlo simulations performed on several different models show that the analytically derived speedup holds.

cond-mat.stat-mech↗