Univerzalnost kvantnih halo stanja

Maričić Zoran

Ovaj rad rigoroznim izvođenjem utvrđuje De Broljevu relaciju λ = h/p iz prvih principa Teorije Vremenske Modulacije (TVM), bez uvođenja naknadnih hipoteza, postuliranih kvantnih uslova ili empirijskih parametara. U standardnoj kvantnoj mehanici, De Broljeva relacija λ = h/p uvedena je 1924. godine kao hipoteza – pretpostavka da čestice materije poseduju talasna svojstva. Iako je kasnije eksperimentalno potvrđena, njena fundamentalna priroda nikada nije objašnjena: zašto čestice imaju talasnu dužinu? Zašto je odnos baš h/p? Odakle potiče dualizam talas-čestica? Polazeći od početnog stanja definisanog u okviru osnovnog rada TVM [1] – stanja čiste energije u minimalnoj zapremini – te jedinog mogućeg mehanizma koji vodi evoluciji početnog stanja u današnji svemir, u radu se dokazuje da talasno-čestični dualizam nije kvantna zagonetka, već direktno i geometrijski nasleđeno svojstvo primarnog stanja svemira. Analizom transformacionih i stacionarnih stanja kodifikovanih kroz jednačine (20) i (20a), pokazano je kako granice akcije ( ħ/2 i ħ ) diktiraju prenos kružnog (rotacionog) kretanja čiste energije u lokalizovani impuls čestice. Matematičkom indukcijom i analizom unutrašnjeg formalizma dokazana je striktna nepromenjivost Planckove konstante h i univerzalnost relacije λ = h/p kroz sve nivoe transformacije.

Boris Kožnjak

J.P. McEvoy, Oscar Sergio Zárate

Petar Stipanović

In this work, the ground state energy and structural properties, of selected small pure and mixed helium clusters, were studied using quantum Monte Carlo methods. They are characterized by the small mass and the weak attractive part of the interaction potential. In free space, for the first time, the binding energy and structural properties of clusters 4^He_N(T↓)M (N ≤ 8,M ≤ 4) were determined. Only 4^HeT↓and 4^He(T↓)_2 seemed to be unstable, while 4^He_2T↓was confirmed as example of quantum halo state. Ground state of other weakly bound dimers and trimers with a radius extending well into the classically forbidden region was explored as well, with the goal to test the predicted universality of quantum halo states. The focus of the study were molecules consisting of T↓, D↓, 3^He, 4^He and alkali atoms, where interaction between particles is much better known than in the case of nuclei, which are traditional examples of quantum halos. The study of realistic systems was supplemented by model calculations in order to analyze how low-energy properties depend on the interaction potential. The use of variational and diffusion Monte Carlo methods enabled very precise calculation of both size and binding energy of the trimers. More convenient scaling variables of binding energy and size were found, so that in the quantum halo regime, all clusters follow almost the same universal line. In addition, it was found that Borromean states separate from tango trimers when the scaled binding energy weakens sufficiently. Furthermore, the effect of reduced dimensionality on self-binding energies and structural properties of clusters 4^He_n (n ≤ 40), in case of adsorption on weakly attractive cesium and strongly attractive graphene, were studied. In the case of graphene, different models of interaction were constructed to test the influence of corrugations and the McLachlan interaction which were shown to be significant. Self-binding energy is significantly lowered, when McLachlan interaction is included. Anisotropy effect slightly strengthen self-binding, but nevertheless affect the assessment whether energy preferred is liquidlike or solidlike structure of small clusters 4^He_n adsorbed on the graphene. Additionally, clusters 4^He_n 3^He adsorbed on cesium were studied to observe the emergence of the edge states of 3^He atom, localized along the contact line of 4^He with a cesium surface, which can be noticed even for such small number of atoms 4^He as n = 3.

Darko Zarić

U ovom se radu koristenjem metoda kvantnog Monte Carla proucavaju osnovna stanja trimera 4He3He23Na i 4He4He23Na, koji predstavljaju slabo vezana stanja. Prvo su određene energije osnovnih stanja i rezultati su uspoređeni s vrijednostima koji su procijenili drugi autori koristeci razlicite metode i potencijale interakcije. Koristeci ciste estimatore difuzijskog Monte Carla određene su srednje kvadratne međucesticne udaljenosti, te prostorne razdiobe za 4He4He23Na. Ispitan je uvjet za halo stanja trimera i procijenjen je njihov položaj u odnosu na univerzalnu liniju.

Milan Odehnal