article published yes Jeremy R. Armstrong author Aksel S. Jensen author Artem Volosniev author 37D278BC-F248-11E8-B48F-1D18A9856A870000-0003-0393-5525 Nikolaj T. Zinner author MiLe department ISTplus - Postdoctoral Fellowships project A few-body cluster is a building block of a many-body system in a gas phase provided the temperature at most is of the order of the binding energy of this cluster. Here we illustrate this statement by considering a system of tubes filled with dipolar distinguishable particles. We calculate the partition function, which determines the probability to find a few-body cluster at a given temperature. The input for our calculations—the energies of few-body clusters—is estimated using the harmonic approximation. We first describe and demonstrate the validity of our numerical procedure. Then we discuss the results featuring melting of the zero-temperature many-body state into a gas of free particles and few-body clusters. For temperature higher than its binding energy threshold, the dimers overwhelmingly dominate the ensemble, where the remaining probability is in free particles. At very high temperatures free (harmonic oscillator trap-bound) particle dominance is eventually reached. This structure evolution appears both for one and two particles in each layer providing crucial information about the behavior of ultracold dipolar gases. The investigation addresses the transition region between few- and many-body physics as a function of temperature using a system of ten dipoles in five tubes. https://research-explorer.ista.ac.at/download/7882/7887/2020_Mathematics_Armstrong.pdf application/pdfno MDPI2020 eng 2227-7390 00053182410002410.3390/math8040484 84 Armstrong, J. R., Jensen, A. S., Volosniev, A., &#38; Zinner, N. T. (2020). Clusters in separated tubes of tilted dipoles. <i>Mathematics</i>. MDPI. <a href="https://doi.org/10.3390/math8040484">https://doi.org/10.3390/math8040484</a> Armstrong JR, Jensen AS, Volosniev A, Zinner NT. 2020. Clusters in separated tubes of tilted dipoles. Mathematics. 8(4), 484. Armstrong, Jeremy R., Aksel S. Jensen, Artem Volosniev, and Nikolaj T. Zinner. “Clusters in Separated Tubes of Tilted Dipoles.” <i>Mathematics</i>. MDPI, 2020. <a href="https://doi.org/10.3390/math8040484">https://doi.org/10.3390/math8040484</a>. J. R. Armstrong, A. S. Jensen, A. Volosniev, and N. T. Zinner, “Clusters in separated tubes of tilted dipoles,” <i>Mathematics</i>, vol. 8, no. 4. MDPI, 2020. Armstrong JR, Jensen AS, Volosniev A, Zinner NT. Clusters in separated tubes of tilted dipoles. <i>Mathematics</i>. 2020;8(4). doi:<a href="https://doi.org/10.3390/math8040484">10.3390/math8040484</a> J.R. Armstrong, A.S. Jensen, A. Volosniev, N.T. Zinner, Mathematics 8 (2020). Armstrong, Jeremy R., et al. “Clusters in Separated Tubes of Tilted Dipoles.” <i>Mathematics</i>, vol. 8, no. 4, 484, MDPI, 2020, doi:<a href="https://doi.org/10.3390/math8040484">10.3390/math8040484</a>. 78822020-05-24T22:01:00Z2026-04-02T14:33:47Z