Linear Response of One-Dimensional Liquid $$^4\hbox {He}$$ to External Perturbations

Motta, Mário; Bertaina, G.; Vitali, Ettore; Galli, D. E.; Rossi, Maurizio

doi:10.1007/s10909-016-1704-8

Cited by 2 publications

(2 citation statements)

References 57 publications

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“…The static density response function is introduced, in linear response theory, as the coefficient of proportionality between a weak static periodic perturbation ṽ(q) and the produced density fluctuation δρ(q) χ(q)ṽ(q), with respect to the equilibrium homogeneous system [36,37]. At zero temperature, it can be computed by carefully evaluating energy differences between perturbed and unperturbed systems [36] or from the first negative moment of S(q, ω) [38]:…”

Section: Static Density Response Functionmentioning

confidence: 99%

Static density response of one-dimensional soft bosons across the clustering transition

Teruzzi

Pini

Rossotti

et al. 2018

J. Phys.: Conf. Ser.

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One-dimensional bosons interacting via a soft-shoulder potential are investigated at zero temperature. The flatness of the potential at short distances introduces a typical length, such that, at relatively high densities and sufficiently strong interactions, clusters are formed, even in the presence of a completely repulsive potential. We evaluate the static density response function of this system across the transition from the liquid to the cluster liquid phases. Such quantity reveals the density modulations induced by a weak periodic external potential, and is maximal at the clustering wavevector. It is known that this response function is proportional to the static structure factor in the classical regime at high temperature, while for this zerotemperature quantum systems, we extract it from the dynamical structure factor evaluated with quantum Monte Carlo methods.

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Section: Static Density Response Functionmentioning

confidence: 99%

Static density response of one-dimensional soft bosons across the clustering transition

Teruzzi

Pini

Rossotti

et al. 2018

J. Phys.: Conf. Ser.

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show abstract

“…The GIFT method has been successfully applied to the study of spectral functions of various zero-temperature quantum systems in different geometries, such as 4 He [10,33,[40][41][42][43][44], 4 He or H absorbed on various substrates [45][46][47][48], 3 He [49,50], hard spheres [34,51,52], soft particles [53][54][55][56], and the Fermi-Hubbard model [57]. Moreover, a finite-temperature version of the GIFT method has been applied to the study of spectral functions for a system of 4 He atoms in which Bose statistics has been suppressed [58].…”

Section: Applications: the Dynamical Structure Factor Of Liquid 4 Hementioning

confidence: 99%

Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo

Bertaina

Galli

Vitali

2017

Advances in Physics: X

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The term analytic continuation emerges in many branches of Mathematics, Physics, and, more generally, applied Science. Generally speaking, in many situations, given some amount of information that could arise from experimental or numerical measurements, one is interested in extending the domain of such information, to infer the values of some variables which are central for the study of a given problem. For example, focusing on Condensed Matter Physics, state-of-the-art methodologies to study strongly correlated quantum physical systems are able to yield accurate estimations of dynamical correlations in imaginary time. Those functions have to be extended to the whole complex plane, via analytic continuation, in order to infer real-time properties of those physical systems. In this Review, we will present the Genetic Inversion via Falsification of Theories method, which allowed us to compute dynamical properties of strongly interacting quantum many-body systems with very high accuracy.Even though the method arose in the realm of Condensed Matter Physics, it provides a very general framework to face analytic continuation problems that could emerge in several areas of applied Science. Here we provide a pedagogical review that elucidates the approach we have developed.passing Quantum Field Theory, Condensed Matter Physics, as well as image reconstruction and many others.A wide family of physical applications of analytic continuations originate from the celebrated Wick rotation, a mapping between real time and imaginary time:whose importance and usefulness is essentially due to mathematical reasons. For example, in the realm of Quantum Field Theory, the Euclidean space-time approach provides much more well-behaved and well-defined expressions than the formulation in Minkowski spacetime [1]. The relation between the two approaches is an analytic continuation problem. Another central example, which will be the topic of this review, arises in Condensed Matter physics. In this context, the Wick rotation provides a mapping between the quantum mechanical evolution operator and the imaginary-time propagator, or thermal density matrix:whereĤ is the Hamiltonian operator of a quantum system and is Planck's constant. As in Quantum Field Theory, calculations involving the imaginary-time propagator are generally more well-behaved, and there exist extremely accurate techniques to compute imaginary-time correlation functions. In particular, most quantum Monte Carlo (QMC) methodologies, which nowadays are crucial for the study of strongly correlated physical systems [2,3], are intrinsically formulated in imaginary time, and yield estimations of correlation functions involving the imaginary-time propagator in Eq.(2). It is thus necessary and, as we will discuss below, very challenging, to perform the analytic continuation necessary to infer real-time properties. Incidentally, we mention another context in which analytic continuation turns out to be extremely useful: the reconstruction of images. Consider, for example, the phase retrie...

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Linear Response of One-Dimensional Liquid $$^4\hbox {He}$$ to External Perturbations

Cited by 2 publications

References 57 publications

Static density response of one-dimensional soft bosons across the clustering transition

Static density response of one-dimensional soft bosons across the clustering transition

Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo

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