Path Integral
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2022 ◽  
Vol 12 (1) ◽  
Tobias Dornheim ◽  
Zhandos A. Moldabekov ◽  
Jan Vorberger ◽  
Burkhard Militzer

AbstractDue to its nature as a strongly correlated quantum liquid, ultracold helium is characterized by the nontrivial interplay of different physical effects. Bosonic $$^4{\text {He}}$$ 4 He exhibits superfluidity and Bose-Einstein condensation. Its physical properties have been accurately determined on the basis of ab initio path integral Monte Carlo (PIMC) simulations. In contrast, the corresponding theoretical description of fermionic $$^3{\text {He}}$$ 3 He is severely hampered by the notorious fermion sign problem, and previous PIMC results have been derived by introducing the uncontrolled fixed-node approximation. In this work, we present extensive new PIMC simulations of normal liquid $$^3{\text {He}}$$ 3 He without any nodal constraints. This allows us to to unambiguously quantify the impact of Fermi statistics and to study the effects of temperature on different physical properties like the static structure factor $$S({\mathbf {q}})$$ S ( q ) , the momentum distribution $$n({\mathbf {q}})$$ n ( q ) , and the static density response function $$\chi ({\mathbf {q}})$$ χ ( q ) . In addition, the dynamic structure factor $$S({\mathbf {q}},\omega )$$ S ( q , ω ) is rigorously reconstructed from imaginary-time PIMC data. From simulations of $$^3{\text {He}}$$ 3 He , we derived the familiar phonon–maxon–roton dispersion function that is well-known for $$^4{\text {He}}$$ 4 He and has been reported previously for two-dimensional $$^3{\text {He}}$$ 3 He films (Nature 483:576–579 (2012)). The comparison of our new results for both $$S({\mathbf {q}})$$ S ( q ) and $$S({\mathbf {q}},\omega )$$ S ( q , ω ) with neutron scattering measurements reveals an excellent agreement between theory and experiment.

Physics ◽  
2022 ◽  
Vol 4 (1) ◽  
pp. 12-20
Sumita Datta ◽  
Vanja Dunjko ◽  
Maxim Olshanii

In this paper, the quantum fluctuations of the relative velocity of constituent solitons in a Gross-Pitaevskii breather are studied. The breather is confined in a weak harmonic trap. These fluctuations are monitored, indirectly, using a two-body correlation function measured at a quarter of the harmonic period after the breather creation. The results of an ab initio quantum Monte Carlo calculation, based on the Feynman-Kac path integration method, are compared with the analytical predictions using the recently suggested approach within the Bogoliubov approximation, and a good agreement is obtained.

2022 ◽  
Vol 52 (1) ◽  
Domenico Napoletani ◽  
Daniele C. Struppa

AbstractWe formalize the notion of isolated objects (units), and we build a consistent theory to describe their evolution and interaction. We further introduce a notion of indistinguishability of distinct spacetime paths of a unit, for which the evolution of the state variables of the unit is the same, and a generalization of the equivalence principle based on indistinguishability. Under a time reversal condition on the whole set of indistinguishable paths of a unit, we show that the quantization of motion of spinless elementary particles in a general potential field can be derived in this framework, in the limiting case of weak fields and low velocities. Extrapolating this approach to include weak relativistic effects, we explore possible experimental consequences. We conclude by suggesting a primitive ontology for the theory of isolated objects.

A. Merdaci ◽  
N. Boudiaf ◽  
L. Chetouani

Exact Green’s function related to a Dirac particle submitted to the combination of Aharonov–Bohm and Coulomb potentials in [Formula: see text]) coordinate space is analytically calculated via path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger model. The energy spectrum as well as the corresponding normalized wave functions are extracted following this approach. The interesting properties of the spinors are thus deduced after symmetrization. According to the symmetric form for Green’s function, it is shown that the non-relativistic limit of the Dirac particle is undertaken with much ease.

2022 ◽  
Chenghan Li ◽  
Gregory A. Voth

Ab initio molecular dynamics (AIMD) has become one of the most popular and robust approaches for modeling complicated chemical, liquid, and material systems. However, the formidable computational cost often limits its widespread application in simulations of the largest scale systems. The situation becomes even more severe in cases where the hydrogen nuclei may be better described as quantized particles using a path integral representation. Here, we present a computational approach that combines machine learning with recent advances in path integral contraction schemes, and we achieve a two-orders-of-magnitude acceleration over direct path integral AIMD simulation while at the same time maintaining its accuracy.

2022 ◽  
Matthew D. Houghton ◽  
Alexander B. Oshin ◽  
Michael J. Acheson ◽  
Evangelos A. Theodorou ◽  
Irene M. Gregory

2022 ◽  
Vol 2022 (1) ◽  
pp. 013101
Pipat Harata ◽  
Prathan Srivilai

Abstract We present a calculation of the grand canonical partition function of a serial metallic island system by the imaginary-time path integral formalism. To this purpose, all electronic excitations in the lead and island electrodes are described using Grassmann numbers. The Coulomb charging energy of the system is represented in terms of phase fields conjugate to the island charges. By the large channel approximation, the tunneling action phase dependence can also be determined explicitly. Therefore, we represent the partition function as a path integral over phase fields with a path probability given in an analytically known effective action functional. Using the result, we also propose a calculation of the average electron number of the serial island system in terms of the expectation value of winding numbers. Finally, as an example, we describe the Coulomb blockade effect in the two-island system by the average electron number and propose a method to construct the quantum stability diagram.

Ding Jia

Abstract An important task faced by all approaches of quantum gravity is to incorporate superpositions and quantify quantum uncertainties of spacetime causal relations. We address this task in 2D. By identifying a global Z2 symmetry of 1+1D quantum gravity, we show that gravitational path integral configurations come in equal amplitude pairs with timelike and spacelike relations exchanged. As a consequence, any two points are equally probable to be timelike and spacelike separated in a universe without boundary conditions. In the context of simplicial quantum gravity we identify a local symmetry of the action which shows that even with boundary conditions causal uncertainties are generically present. Depending on the boundary conditions, causal uncertainties can still be large and even maximal.

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