Bose Gas in Classical Environment at Low Temperatures


  • V. Pastukhov Ivan Franko National University of Lviv, Department for Theoretical Physics



dilute Bose gas, weak non-Gaussian disorder, superfluid properties


The properties of a dilute Bose gas with the non-Gaussian quenched disorder are analyzed. Being more specific, we have considered a system of bosons immersed in the classical bath consisting of the non-interacting particles with infinite mass. Making use of perturbation theory up to the second order, we have studied the impact of environment on the ground-state thermodynamic and superfluid characteristics of the Bose component.


M.P.A. Fisher, P.B. Weichman, G. Grinstein, D.S. Fisher. Boson localization and the superfluid-insulator transition. Phys. Rev. B 40, 546 (1989).

M.P.A. Fisher, D.S. Fisher. Onset of superfluidity in random media. Phys. Rev. Lett. 61, 1847 (1988).

K. Huang, H.F. Meng. Hard-sphere Bose gas in random external potentials. Phys. Rev. Lett. 69, 644 (1992).

C.A. M¨uller, C. Gaul. Condensate deformation and quantum depletion of Bose-Einstein condensates in external potentials. New J. Phys. 14, 075025 (2012).

V.I. Yukalov, R. Graham. Bose-Einstein-condensed systems in random potentials. Phys. Rev. A 75, 023619 (2007).

P. Navez, A. Pelster, R. Graham. Bose condensed gas in strong disorder potential with arbitrary correlation length. Appl. Phys. B 86, 395 (2007).

V.I. Yukalov, E.P. Yukalova, K.V. Krutitsky, R. Graham. Bose-Einstein-condensed gases in arbitrarily strong random potentials. Phys. Rev. A 76, 053623 (2007).

G.E. Astrakharchik, J. Boronat, J. Casulleras, S. Giorgini. Superfluidity versus Bose-Einstein condensation in a Bose gas with disorder. Phys. Rev. A 66, 023603 (2002).

M. Kobayashi, M. Tsubota. Bose-Einstein condensation and superfluidity of a dilute Bose gas in a random potential. Phys. Rev. B 66, 174516 (2002).

G.M. Falco, A. Pelster, R. Graham. Thermodynamics of a Bose-Einstein condensate with weak disorder. Phys. Rev. A 75, 063619 (2007).

T. Khellil, A. Pelster. Hartree-Fock mean-field theory for trapped dirty bosons. J. Stat. Mech. 2016, 063301 (2016).

O. Zobay. Condensation temperature of interacting Bose gases with and without disorder. Phys. Rev. A 73, 023616 (2006).

M. Timmer, A. Pelster, R. Graham. Disorder-induced shift of condensation temperature for dilute trapped Bose gases. EPL (Europhysics Letters) 76, 760 (2006).

S. Pilati, S. Giorgini, N. Prokof'ev. Superfluid transition in a Bose gas with correlated disorder. Phys. Rev. Lett. 102, 150402 (2009).

S. Giorgini, L. Pitaevskii, S. Stringari. Effects of disorder in a dilute Bose gas. Phys. Rev. B 49, 12938 (1994).

C. Gaul, C. A.M¨uller. Bogoliubov excitations of disordered Bose-Einstein condensates. Phys. Rev. A 83, 063629 (2011).

P. Lugan, L. Sanchez-Palencia. Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder. Phys. Rev. A 84, 013612 (2011).

S. Lellouch, L.-K. Lim, L. Sanchez-Palencia. Propagation of collective pair excitations in disordered Bose superfluids. Phys. Rev. A 92, 043611 (2015).

M. Boninsegni, H.R. Glyde. Excitations of liquid 4He in disorder. J. Low Temp. Phys. 112, 251 (1998).

H.R. Glyde, B. F˚ak, O. Plantevin. Excitations of liquid 4He in disorder. J. Low Temp. Phys. 113, 537 (1998).

A.V. Lopatin, V.M. Vinokur. Thermodynamics of the superfluid dilute Bose gas with disorder. Phys. Rev. Lett. 88, 235503 (2002).

C.A. M¨uller. Josephson relation for disordered superfluids. Phys. Rev. A 91, 023602 (2015).

G. Semeghini, M. Landini, P. Castilho, S. Roy, G. Spagnolli, A. Trenkwalder, M. Fattori, M. Inguscio, G. Modugno. Measurement of the mobility edge for 3D Anderson localization. Nature Phys. 11, 554 (2015).

B. Abdullaev, A. Pelster. Bose-Einstein condensate in weak 3d isotropic speckle disorder. Eur. Phys. J. D 66, 314 (2012).

G.E. Astrakharchik, K.V. Krutitsky, P. Navez. Phase diagram of quasi-two-dimensional bosons in a laser-speckle potential. Phys. Rev. A 87, 061601(R) (2013).

E. Fratini, S. Pilati. Anderson localization of matter waves in quantum-chaos theory. Phys. Rev. A 91, 061601(R) (2015).

V.N. Popov. Functional Integrals and Collective Excitations (Cambridge Univ. Press, 1987).

V. Pastukhov. High-density limit of quasi-two-dimensional dipolar Bose gas. Ann. Phys. 372, 149 (2016).

V. Pastukhov. Damping of Bogoliubov excitations at finite temperatures. J. Phys. A: Math. Theor. 48, 405002 (2015).

V. Pastukhov. Infrared behavior of dipolar Bose systems at low temperatures. J. Low Temp. Phys. 186, 148 (2017).

A.F. Andreev, E.P. Bashkin. Three-velocity hydrodynamics of superfluid solutions. Zh. Eksp. Teor. Fiz. 69, 319 (1975), [Sov. Phys. JETP 42, 164 (1975)].

L. Viverit, S. Giorgini. Ground-state properties of a dilute Bose-Fermi mixture. Phys. Rev. A 66, 063604 (2002).

V. Pastukhov. Beyond mean-field properties of binary dipolar Bose mixtures at low temperatures. Phys. Rev. A 95, 023614 (2017).

O.I. Utesov, M.I. Baglay, S.V. Andreev. Effective interactions in a quantum Bose-Bose mixture. Phys. Rev. A 97, 053617 (2018).

P. Konietin, V. Pastukhov. 2D dilute Bose mixture at low temperatures. J. Low Temp. Phys. 190, 256 (2018).

L.D. Landau, E.M. Lifshitz. Statistical Physics Part 2: Theory of Condensed State, (Pergamon Press, 1981).

G.E. Astrakharchik, L.P. Pitaevskii. Motion of a heavy impurity through a Bose-Einstein condensate. Phys. Rev. A 70, 013608 (2004).

T.D. Lee, K. Huang, C.N. Yang. Eigenvalues and eigen-functions of a Bose system of hard spheres and its low-temperature properties. Phys. Rev. 106, 1135 (1957).

N.M. Hugenholtz, D. Pines. Ground-state energy and excitation spectrum of a system of interacting bosons. Phys. Rev. 116, 489 (1959).

N. Navon, S. Nascimb'ene, F. Chevy, C. Salomon. The equation of state of a low-temperature Fermi gas with tunable interactions. Science 328, 729 (2010).




How to Cite

Pastukhov, V. (2020). Bose Gas in Classical Environment at Low Temperatures. Ukrainian Journal of Physics, 65(11), 1002.



General physics