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We consider a variational approach to the Bose-Hubbard model based on Bogoliubov theory. We introduce the grand canonical and canonical free energy functional for which we prove the existence of minimizers. By analyzing their structure we show the existence of a superfluid-Mott insulator phase transition at positive temperatures. In particular, we show that this model does not exhibit a quantum phase transition., Comment: 35 pages, 2 figures

We consider the spin-orbit coupled Bose gas with repulsive mean-field interparticle interactions. We analyze the phase diagram of the system varying the temperature $T>0$, the chemical potentials, as well as interparticle and spin-orbit interaction couplings. Our results indicate that, for Rashba- and Weyl-type spin-orbit couplings, condensates featuring ordering wavevector $\vec{Q}\neq \vec{0}$ are fragile with respect to thermal fluctuations and, at $T>0$, the only stable thermodynamic phases involving the Bose-Einstein condensate (BEC) are those of uniform type with $\vec{Q}=\vec{0}$. On the other hand, presence of the spin-orbit coupling stabilizes the $\vec{Q}=\vec{0}$ BEC state at any dimensionality $d>1$ and modifies either the order or the universality class of the corresponding phase transition. We emphasize the singular nature of the limit of vanishing spin-orbit interaction coupling $v$, sizable shifts of the phase boundaries upon varying $v$, as well as the role of the relative magnitudes of the interparticle interaction couplings for the character of the condensation transition.

We propose a simple model of an interacting, fully spin--polarized Fermi gas in dimensions $d=2$ and $d=3$, and derive the approximate expression for the energy spectrum and the corresponding formula for the Helmholtz free energy. We analyze the thermodynamics of the system and find the lines of first--order phase transitions between the low and high density phases terminating at critical points. The properties of the corresponding phase diagrams are qualitatively different for $d=2$ and $3$, and sensitively depend on the interparticle attraction, which marks a departure from the standard van der Waals theory. The differences originate from the Pauli exclusion principle and are embeded in the fermionic nature of the system under study., Comment: 10 pages, 11 figures

The Gamow-Teller strength distribution covering the entire $\beta$-decay window, up to 10.312(4) MeV, of $^{80g+m}$Ga was measured for the first time in photo-fission of UC$_x$ induced by 50 MeV electron beam. The new data show significant enhancement in the high-energy region with a jump-structure. Simultaneously, the $\gamma$ de-exciting behavior of $\beta$-populated states presents a competition between de-excitation to 2$_1^+$ [$\beta_2$ = 0.155(9)] and to 2$_2^+$ [$\beta_2$ = 0.053$_{0.009}^{0.008}$)] in $^{80}$Ge. Based on these facts and combined with a realistic shell model calculation and systematic analysis of logft ratio between precursor $\beta$-decay to 2$_2^+$ and to 2$_1^+$ of Ga isotopes, we conclude that these phenomena evidence simultaneous impacts of nuclear shell structure and collectivity on B(GT) and its distribution and, therefore, the half-life of the precursor. These data prove that the nucleus as a multi-nucleon correlated quantum system reacts as a whole when $\beta$-decay occurs in contrast to simple single-particle excitation. Additionally, the comparison with the theoretical results evidence how challenging is the description of the experimental data obtained, and render this experimental outcome a sound test for the theoretical models.

We address the possibility of realizing Bose-Einstein condensation as a first-order phase transition by admixture of particles of different species. To this aim we perform a comprehensive analysis of phase diagrams of two-component mixtures of bosons at finite temperatures. As a prototype model, we analyze a binary mixture of Bose particles interacting via an infinite-range (Kac-scaled) two-body potential. We obtain a rich phase diagram, where the transition between the normal and Bose-Einstein condensed phases may be either continuous or first-order. The phase diagram hosts lines of triple points, tricritical points, as well as quadruple points. We address the structure of the phase diagram depending on the relative magnitudes of the inter- and intra-species interaction couplings. In addition, even for purely repulsive interactions, we identify a first-order liquid-gas type transition between non-condensed phases characterized by different particle concentrations. In the obtained phase diagram, a surface of such first-order transitions terminates with a line of critical points., Comment: 10 pages, 10 figures

According to the Bogoliubov theory the low energy behaviour of the Bose gas at zero temperature can be described by non-interacting bosonic quasiparticles called phonons. In this work the damping rate of phonons at low momenta, the so-called Beliaev damping, is explained and computed with simple arguments involving the Fermi Golden Rule and Bogoliubov's quasiparticles., Comment: 27 pages, 2 figures, revised version

We consider an ideal Bose gas enclosed in a $d$-dimensional slab of thickness $D$. Using the grand canonical ensemble we calculate the variance of the thermal Casimir force acting on the slab's walls. The variance evaluated per unit wall area is shown to decay like $ \Delta_{var}/D$ for large $D$. The amplitude $ \Delta_{var}$ is a non-universal function of two scaling variables $\lambda/ \xi$ and $D/ \xi$, where $\lambda$ is the thermal de Broglie wavelength and $\xi$ is the bulk correlation length. It can be expressed via the bulk pressure, the Casimir force per unit wall area, and its derivative with respect to chemical potential. For thermodynamic states corresponding to the presence of the Bose-Einstein condensate the amplitude $ \Delta_{var}$ retains its non-universal character while the ratio of the mean standard deviation and the Casimir force takes the scaling form $(D/L)^{\frac{d-1}{2}}\, (D/\lambda)^{d/2}$, where $L$ is the linear size of the wall., Comment: 9 pages, no figures

High-resolution gamma-ray spectroscopy of 18N is performed with the Advanced GAmma Tracking Array AGATA, following deep-inelastic processes induced by an 18O beam on a 181Ta target. Six states are newly identified, which together with the three known excitations exhaust all negative-parity excited states expected in 18N below the neutron threshold. Spin and parities are proposed for all located states on the basis of decay branchings and comparison with large-scale shell-model calculations performed in the p-sd space, with the YSOX interaction. Of particular interest is the location of the 0^-_1 and 1^-_2 excitations, which provide strong constrains for cross-shell p-sd matrix elements based on realistic interactions, and help to simultaneously reproduce the ground and first-excited states in 16N and 18N, for the first time. Understanding the 18N structure may also have significant impact on neutron-capture cross-section calculations in r-process modeling including light neutron-rich nuclei.

We analyze the thermodynamic Casimir effect occurring in a gas of non-interacting bosons confined by two parallel walls with a strongly anisotropic dispersion inherited from an underlying lattice. In the direction perpendicular to the confining walls the standard quadratic dispersion is replaced by the term $|{\bf p}|^{\alpha}$ with $\alpha \geq 2$ treated as a parameter. We derive a closed, analytical expression for the Casimir force depending on the dimensionality $d$ and the exponent $\alpha$, and analyze it for thermodynamic states in which the Bose-Einstein condensate is present. For $\alpha\in\{4,6,8,\dots\}$ the exponent governing the decay of the Casimir force with increasing distance between the walls becomes modified and the Casimir amplitude $\Delta_{\alpha}(d)$ exhibits oscillations of sign as a function of $d$. Otherwise we find that $\Delta_{\alpha}(d)$ features singularities when viewed as a function of $d$ and $\alpha$. Recovering the known previous results for the isotropic limit $\alpha=2$ turns out to occur via a cancellation of singular terms., Comment: 15 pages, 3 figures

The success of Gross--Pitevskii and Bogoliubov theories in the description of large systems of interacting bosons led to a substantial effort into rigorously deriving these effective theories. In this work we shall review the related existing literature in the context of dynamics of large bosonic systems., Comment: A contribution to the Proceedings of the Workshop on Density Functionals for Many-Particle Systems, September 2019, Singapore; 38 pages

A novel Monte Carlo technique has been developed to determine lifetimes of excited states in the tens-to-hundreds femtoseconds range. The method is applied to low-energy heavy-ion binary reactions populating nuclei with complex velocity distributions. Its relevance is demonstrated in connection with the $^{18}$O(7.0 MeV/u) + $^{181}$Ta experiment, performed at GANIL with the AGATA+VAMOS+PARIS setup, to study neutron-rich O, C, N, ... nuclei. Excited states in $^{17}$O and $^{19}$O, with known lifetimes, are used to validate the method over the $\sim$20-400 fs lifetime-sensitivity range. Emphasis is given to the unprecedented position resolution provided by $\gamma$-tracking arrays, which turns out to be essential for reaching the required accuracy in Doppler-shift correction, at the basis of the detailed analysis of $\gamma$-ray lineshape and resulting state lifetime determination. The technique is anticipated to be an important tool for lifetime investigations in exotic neutron-rich nuclei, produced with intense ISOL-type beams.

We consider the homogeneous Bose gas on a unit torus in the mean-field regime when the interaction strength is proportional to the inverse of the particle number. In the limit when the number of particles becomes large, we derive a two-term expansion of the one-body density matrix of the ground state. The proof is based on a cubic correction to Bogoliubov's approximation of the ground state energy and the ground state., Comment: 30 pages, revised version, to appear in Calc. Var. PDE

To test the predictive power of ab initio nuclear structure theory, the lifetime of the second 2+ state in neutron-rich 20O, tau(2+_2 ) = 150(+80-30) fs, and an estimate for the lifetime of the second 2+ state in 16C have been obtained, for the first time. The results were achieved via a novel Monte Carlo technique that allowed us to measure nuclear state lifetimes in the tens-to-hundreds femtoseconds range, by analyzing the Doppler-shifted gamma-transition line shapes of products of low-energy transfer and deep-inelastic processes in the reaction 18O (7.0 MeV/u) + 181Ta. The requested sensitivity could only be reached owing to the excellent performances of the AGATA gamma-tracking array, coupled to the PARIS scintillator array and to the VAMOS++ magnetic spectrometer. The experimental lifetimes agree with predictions of ab initio calculations using two- and three-nucleon interactions, obtained with the valence-space in-medium similarity renormalization group for 20O, and with the no-core shell model for 16C. The present measurement shows the power of electromagnetic observables, determined with high-precision gamma spectroscopy, to assess the quality of first-principles nuclear structure calculations, complementing common benchmarks based on nuclear energies. The proposed experimental approach will be essential for short lifetimes measurements in unexplored regions of the nuclear chart, including r-process nuclei, when intense ISOL-type beams become available.

We study the Bose-Einstein condensates of trapped Bose gases in the Gross-Pitaevskii regime. We show that the ground state energy and ground states of the many-body quantum system are correctly described by the Gross-Pitaevskii equation in the large particle number limit, and provide the optimal convergence rate. Our work extends the previous results of Lieb, Seiringer and Yngvason on the leading order convergence, and of Boccato, Brennecke, Cenatiempo and Schlein on the homogeneous gas. Our method relies on the idea of 'completing the square', inspired by recent works of Brietzke, Fournais and Solovej on the Lee-Huang-Yang formula, and a general estimate for Bogoliubov quadratic Hamiltonians on Fock space., Comment: Final version to appear in Analysis & PDE

We consider the ferromagnetic quantum Heisenberg model in one dimension, for any spin $S\geq 1/2$. We give upper and lower bounds on the free energy, proving that at low temperature it is asymptotically equal to the one of an ideal Bose gas of magnons, as predicted by the spin-wave approximation. The trial state used in the upper bound yields an analogous estimate also in the case of two spatial dimensions, which is believed to be sharp at low temperature., Comment: LaTeX, 22 pages; revised version

Within mean-field theory we study wetting of elastic substrates. Our analysis is based on a grand canonical free energy functional of the fluid number density and of the substrate displacement field. The substrate is described in terms of the linear theory of elasticity, parametrized by two Lam\'e coefficients. The fluid contribution is of the van der Waals type. Two potentials characterize the interparticle interactions in the system. The long-ranged attraction between the fluid particles is described by a potential $w(r)$, and $v(r)$ characterizes the substrate-fluid interaction. By integrating out the elastic degrees of freedom we obtain an effective theory for the fluid number density alone. Its structure is similar to the one for wetting of an inert substrate. However, the potential $w(r)$ is replaced by an effective potential which, in addition to $w(r)$, contains a term bilinear in $v(r)$. We discuss the corresponding wetting transitions in terms of an effective interface potential $\omega(\ell)$, where $\ell$ denotes the thickness of the wetting layer. We show that in the case of algebraically decaying interactions the elasticity of the substrate may suppress critical wetting transitions, and may even turn them first order.

We analyze the Casimir forces for an ideal Bose gas enclosed between two infinite parallel walls separated by the distance D. The walls are characterized by the Dirichlet boundary conditions. We show that if the thermodynamic state with Bose-Einstein condensate present is correctly approached along the path pertinent to the Dirichlet b.c. then the leading term describing the large-distance decay of thermal Casimir force between the walls is 1/D^2 with a non-universal amplitude. The next order correction is lnD/D^3. These observations remain in contrast with the decay law for both the periodic and Neumann boundary conditions for which the leading term is 1/D^3 with a universal amplitude. We associate this discrepancy with the non-zero D-dependent positive value of the one-particle ground state energy in the case of Dirichlet boundary conditions.

We extend the analysis of the Bogoliubov free energy functional to two dimensions at very low temperatures. For sufficiently weak interactions, we prove two term asymptotics for the ground state energy., Comment: revised version

We discuss thermodynamic properties of harmonically trapped imperfect quantum gases. The spatial inhomogeneity of these systems imposes a redefinition of the mean-field interparticle potential energy as compared to the homogeneous case. In our approach, it takes the form $\frac{a}{2} N^2 \, \omega^d$, where $N$ is the number of particles, $\omega$ - the harmonic trap frequency, $d$ - system's dimensionality, and $a$ is a parameter characterizing the interparticle interaction. We provide arguments that this model corresponds to the limiting case of a long-ranged interparticle potential of vanishingly small amplitude. This conclusion is drawn from a computation similar to the well-known Kac scaling procedure, which is presented here in a form adapted to the case of an isotropic harmonic trap. We show that within our model, the imperfect gas of trapped repulsive bosons undergoes the Bose-Einstein condensation provided $d>1$. The main result of our analysis is that in $d=1$ the gas of attractive imperfect fermions with $a=-a_{F}<0$ is thermodynamically equivalent to the gas of repulsive bosons with $a=a_{B}>0$ provided the parameters $a_{F}$ and $a_{B}$ fulfill the relation $a_{B}+a_{F}=\hbar$. This result supplements similar recent conclusion about thermodynamic equivalence of two-dimensional uniform imperfect repulsive Bose and attractive Fermi gases., Comment: Revised version, comments added

Bosonic quadratic Hamiltonians, often called Bogoliubov Hamiltonians, play an important role in the theory of many-boson systems where they arise in a natural way as an approximation to the full many-body problem. In this note we would like to give an overview of recent advances in the study of bosonic quadratic Hamiltonians. In particular, we relate the reported results to what can be called the time-dependent diagonalization problem., Comment: to appear in "Macroscopic Limits of Quantum Systems", Springer Proceedings in Mathematics and Statistics

We consider a system of $N$ bosons interacting through a singular two-body potential scaling with $N$ and having the form $N^{3\beta-1} V (N^\beta x)$, for an arbitrary parameter $\beta \in (0,1)$. We provide a norm-approximation for the many-body evolution of initial data exhibiting Bose-Einstein condensation in terms of a cubic nonlinear Schr\"odinger equation for the condensate wave function and of a unitary Fock space evolution with a generator quadratic in creation and annihilation operators for the fluctuations., Comment: 37 pages; final version, to appear in Annales de l'Institut Henri Poincare - Analyse non lineaire

We study the norm approximation to the Schr\"odinger dynamics of $N$ bosons in $\mathbb{R}^d$ ($d=1,2$) with an interaction potential of the form $N^{d\beta-1}w(N^{\beta}(x-y))$. Here we are interested in the focusing case $w\le 0$. Assuming that there is complete Bose-Einstein condensation in the initial state, we show that in the large $N$ limit, the evolution of the condensate is effectively described by a nonlinear Schr\"odinger equation and the evolution of the fluctuations around the condensate is governed by a quadratic Hamiltonian, resulting from Bogoliubov approximation. Our result holds true for all $\beta>0$ when $d=1$ and for all $0<\beta<1$ when $d=2$.

Following an earlier calculation in 3D, we calculate the 2D critical temperature of a dilute, translation-invariant Bose gas using a variational formulation of the Bogoliubov approximation introduced by Critchley and Solomon in 1976. This provides the first analytical calculation of the Kosterlitz-Thouless transition temperature that includes the constant in the logarithm., Comment: Published version, 7 pages, 2 figures

We consider two-dimensional imperfect attractive Fermi and repulsive Bose gases consisting of spinless point particles whose total interparticle interaction energy is represented by $a N^2/2 V$ with $a=-a_{F}\leq 0$ for fermions, and $a=a_{B}\geq 0$ for bosons. We show that in spite of the attraction the thermodynamics of $d=2$ imperfect Fermi gas remains well defined for $0 \leq a_{F}\leq a_{0}=h^2/2\pi m$, and is exactly the same as the one of the repulsive imperfect Bose gas with $a_{B}=a_{0}-a_{F}$. In particular, for $a_{F}=a_{0}$ one observes the thermodynamic equivalence of the attractive imperfect Fermi gas and the ideal Bose gas., Comment: 5 pages, 1 figure

We describe theoretically and validate experimentally the mechanism of formation of capillary bridges during pulling a beaded chain out from a liquid with a planar surface. There are two types of capillary bridges present in this system, namely the sphere-planar liquid surface bridge initially formed between the spherical bead leaving the liquid bath and the original bulk planar liquid surface, and the sphere-sphere capillary bridge formed between neighbouring beads in the part of the chain above the liquid surface. During pulling the chain out of the liquid, the sphere-planar liquid surface bridge transforms into the sphere-sphere bridge. We show that for monodisperse spherical beads comprising the chain, this morphological phase transition can be either continuous or discontinuous. The transition is continuous when the diameter of the spherical beads is larger than the capillary length. Otherwise, the transition is discontinuous, likewise the capillary force acting on the chain., Comment: 10 pages, 14 figures

We review some recent results on the norm approximation to the Schr\"odinger dynamics. We consider $N$ bosons in $\mathbb{R}^3$ with an interaction potential of the form $N^{3\beta-1}w(N^{\beta}(x-y))$ with $0\le \beta<1/2$, and show that in the large $N$ limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation., Comment: A contribution for the volume "Advances in Quantum Mechanics: contemporary trends and open problems" of the INdAM-Springer series

In order to understand the performance of the PARIS (Photon Array for the studies with Radioactive Ion and Stable beams) detector, detailed characterization of two individual phoswich (LaBr$_3$(Ce)-NaI(Tl)) elements has been carried out. The detector response is investigated over a wide range of $E_{\gamma}$ = 0.6 to 22.6 MeV using radioactive sources and employing $^{11}B(p,\gamma)$ reaction at $E_p$ = 163 keV and $E_p$ = 7.2 MeV. The linearity of energy response of the LaBr$_3$(Ce) detector is tested upto 22.6 MeV using three different voltage dividers. The data acquisition system using CAEN digitizers is set up and optimized to get the best energy and time resolution. The energy resolution of $\sim$ 2.1% at $E_\gamma$ = 22.6~MeV is measured for the configuration giving best linearity upto high energy. Time resolution of the phoswich detector is measured with a $^{60}$Co source after implementing CFD algorithm for the digitized pulses and is found to be excellent (FWHM $\sim$ 315~ps). In order to study the effect of count rate on detectors, the centroid position and width of the $E_{\gamma}$ = 835~keV peak were measured upto 220 kHz count rate. The measured efficiency data with radioactive sources are in good agreement with GEANT4 based simulations. The total energy spectrum after the add-back of energy signals in phoswich components is also presented., Comment: Accepted in JINST

We study the norm approximation to the Schr\"odinger dynamics of $N$ bosons in $\mathbb{R}^3$ with an interaction potential of the form $N^{3\beta-1}w(N^{\beta}(x-y))$. Assuming that in the initial state the particles outside of the condensate form a quasi-free state with finite kinetic energy, we show that in the large $N$ limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation for all $0\le \beta<1/2$. The range of $\beta$ is expected to be optimal for this large class of initial states., Comment: Final version, to appear in Journal de Math\'ematiques Pures et Appliqu\'ees

The electromagnetic structure of $^{140}$Sm was studied in a low-energy Coulomb excitation experiment with a radioactive ion beam from the REX-ISOLDE facility at CERN. The $2^+$ and $4^+$ states of the ground-state band and a second $2^+$ state were populated by multi-step excitation. The analysis of the differential Coulomb excitation cross sections yielded reduced transition probabilities between all observed states and the spectroscopic quadrupole moment for the $2_1^+$ state. The experimental results are compared to large-scale shell model calculations and beyond-mean-field calculations based on the Gogny D1S interaction with a five-dimensional collective Hamiltonian formalism. Simpler geometric and algebraic models are also employed to interpret the experimental data. The results indicate that $^{140}$Sm shows considerable $\gamma$ softness, but in contrast to earlier speculation no signs of shape coexistence at low excitation energy. This work sheds more light on the onset of deformation and collectivity in this mass region., Comment: 15 pages, 12 figures

We consider two-dimensional Ising strip bounded by two planar, inhomogeneous walls. The inhomogeneity of each wall is modeled by a magnetic field acting on surface spins. It is equal to $+h_1$ except for a group of $N_1$ sites where it is equal to $-h_1$. The inhomogeneities of the upper and lower wall are shifted with respect to each other by a lateral distance $L$. Using exact diagonalization of the transfer matrix, we study both the lateral and normal critical Casimir forces as well as magnetization profiles for a wide range of temperatures and system parameters. The lateral critical Casimir force tends to reduce the shift between the inhomogeneities, and the excess normal force is attractive. Upon increasing the shift $L$ we observe, depending on the temperature, three different scenarios of breaking of the capillary bridge of negative magnetization connecting the inhomogeneities of the walls across the strip. As long as there exists a capillary bridge in the system, the magnitude of the excess total critical Casimir force is almost constant, with its direction depending on $L$. By investigating the bridge morphologies we have found a relation between the point at which the bridge breaks and the inflection point of the force. We provide a simple argument that some of the properties reported here should also hold for a whole range of different models of the strip with the same type of inhomogeneity.

We study the Casimir effect in the vicinity of a quantum critical point. As a prototypical system we analyze the $d$-dimensional imperfect (mean-field) Bose gas enclosed in a slab of extension $L^{d-1}\times D$ and subject to periodic boundary conditions. The thermodynamic state is adjusted so that $L\gg\lambda\gg D\gg\l_{mic}$, where $\lambda\sim T^{-1/2}$ is the thermal de Broglie length, and $l_{mic}$ denotes microscopic lengthscales. Our exact analysis indicates that the Casimir force in the above specified regime is generically repulsive and decays either algebraically or exponentially, with a non-universal amplitude.

We analyse the canonical Bogoliubov free energy functional at low temperatures in the dilute limit. We prove existence of a first order phase transition and, in the limit $a_0\to a$, we determine the critical temperature to be $T_{\rm{c}}=T_{\rm{fc}}(1+1.49(\rho^{1/3}a))$ to leading order. Here, $T_{\rm{fc}}$ is the critical temperature of the free Bose gas, $\rho$ is the density of the gas, $a$ is the scattering length of the pair-interaction potential $V$, and $a_0=(8\pi)^{-1}\widehat{V}(0)$ its first order approximation. We also prove asymptotic expansions for the free energy. In particular, we recover the Lee-Huang-Yang formula in the limit $a_0\to a$., Comment: Published version, 58 pages, 2 figures

The Bogoliubov free energy functional is analysed. The functional serves as a model of a translation invariant Bose gas at positive temperature. We prove the existence of minimizers in the case of repulsive interactions given by a sufficiently regular two-body potential. Furthermore, we prove existence of a phase transition in this model and provide its phase diagram., Comment: Published version, 54 pages, 1 figure

We consider the dynamics of a large quantum system of $N$ identical bosons in 3D interacting via a two-body potential of the form $N^{3\beta-1} w(N^\beta(x-y))$. For fixed $0\leq \beta <1/3$ and large $N$, we obtain a norm approximation to the many-body evolution in the $N$-particle Hilbert space. The leading order behaviour of the dynamics is determined by Hartree theory while the second order is given by Bogoliubov theory., Comment: Final version, to appear in ATMP

We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our sufficient conditions are optimal in the sense that they become necessary when the relevant one-body operators commute., Comment: Revised version to appear in Journal of Functional Analysis

With the recent advances in radioactive ion beam technology, Coulomb excitation at safe energies becomes an important experimental tool in nuclear-structure physics. The usefulness of the technique to extract key information on the electromagnetic properties of nuclei has been demonstrated since the 1960's with stable beam and target combinations. New challenges present themselves when studying exotic nuclei with this technique, including dealing with low statistics or number of data points, absolute and relative normalisation of the measured cross sections and a lack of complimentary experimental data, such as excited-state lifetimes and branching ratios. This paper addresses some of these common issues and presents analysis techniques to extract transition strengths and quadrupole moments utilising the least-squares fit code, {\rmfamily \textsc{gosia}}., Comment: 14 pages, 10 figures, to be published in European Physical Journal A

We consider two-dimensional ($d=2$) systems with short-ranged microscopic interactions, where interface unbinding (wetting) transitions occur in the limit of vanishing temperature $T$. For $T=0$ the transition is characterized by non-universal critical properties analogous to those established for thermal wetting transitions in $d=3$, albeit with a redefined capillary parameter $\tilde{\omega}$. Within a functional renormalization-group treatment of an effective interfacial model, we compute the finite temperature phase diagram, exhibiting a line of interface unbinding transitions, terminating at $T=0$ with an interfacial quantum critical point. At finite $T$ we identify distinct scaling regimes, reflecting the interplay between quantum and thermal interfacial fluctuations. A crossover line marking the onset of the quantum critical regime is described by the $d=3$ interfacial correlation-length exponent $\nu_{||}$. This opens a new way to investigate the non-universal character of $\nu_{||}$ without penetrating the true critical regime. On the other hand, the emergent interfacial quantum critical regime shows no signatures of non-universality.

This thesis is devoted to a rigorous study of interacting quantum gases. The main objects of interest are the closely related concepts of excitation spectrum and quasiparticles. The immediate motivation of this work is to propose a spectral point of view concerning these two concepts. In the first part of this thesis we discuss the concepts of excitation spectrum and quasiparticles. We provide an overview of physical motivations and based on that we propose a spectral and Hamiltonian-based approach towards these terms. Based on that, we formulate definitions and propositions related to these concepts. In the second part we recall the Bogoliubov and Hartree-Fock-Bogoliubov approximations, which in the physics literature are used to obtain the quasiparticle picture. We show how these two approaches fit into a universal scheme which allows us to arrive at a quasiparticle picture in a more general setup. This scheme is based on the minimization of Hamiltonians over the so-called Gaussian states. Its abstract formulation is the content of Beliaev's Theorem. In the last part we present a rigorous result concerning the justification of the Bogoliubov approximation. This justification employs the concept of the mean-field and infinite-volume limit. We show that for a large number of particles, a large volume and a sufficiently high density, the low-lying energy-momentum spectrum of the homogeneous Bose gas is well described by the Bogoliubov approximation. This result, which is formulated in the form of a theorem, can be seen as the main result of this thesis., Comment: PhD Thesis, University of Warsaw, 2014

We analyze the lateral critical Casimir force acting between two planar, chemically inhomogeneous walls confining an infinite 2D Ising strip of width $M$. The inhomogeneity of each of the walls has size $N_1$; they are shifted by the distance $L$ along the strip. Using the exact diagonalization of the transfer matrix, we calculate the lateral critical Casimir force and discuss its properties, in particular its scaling close to the 2D bulk critical point, as a function of temperature, surface magnetic field, and the geometric parameters $M$, $N_1$, $L$. We determine the magnetization profiles which display the formation of the bridge joining the inhomogeneities on the walls and establish the relation between the characteristic properties of the lateral Casimir force and magnetization morphologies. We check numerically that breaking of the bridge is related to the inflection point of the lateral force., Comment: 5 pages, 6 figures

We study the low-temperature limit of the d-dimensional imperfect Bose gas. Relying on an exact analysis of the microscopic model, we establish the existence of a second-order quantum phase transition to a phase involving the Bose-Einstein condensate. The transition is triggered by varying the chemical potential and persists at non-zero temperatures T for d>2. We extract the exact phase diagram and identify the scaling regimes in the vicinity of the quantum critical point focusing on the behavior of the correlation length \xi. The length \xi develops an essential singularity exclusively for d=2. We follow the evolution of the phase diagram varying d. For d>2 our results agree with renormalization-group based analysis of the effective bosonic order-parameter models with the dynamical exponent z=2., Comment: 10 pages, 2 figures; version (almost) as published

The morphological phase transition between a sessile and lenticular shapes of a droplet placed in a nanochannel is observed upon increasing the droplet volume. The phase diagram for this system is discussed within the macro- and mesoscopic approaches. On the mesoscopic level, the van der Waals forces are taken into account via the effective interface potential acting between the channel walls and the droplet. We discuss the contact angle dependence on the droplet volume and the distance between the walls; this angle turns out to be smaller than the macroscopic Young's angle. The droplet presence induces the solvation force acting between the channel walls. It can be both attractive and repulsive, depending on the width of the channel., Comment: 13 pages, 18 figures

We consider the d-dimensional imperfect (mean-field) Bose gas confined in a slit-like geometry and subject to periodic boundary conditions. Within an exact analytical treatment we first extract the bulk critical properties of the system at Bose-Einstein condensation and identify the bulk universality class to be the one of the classical d-dimensional spherical model. Subsequently we consider finite slit width D and analyze the excess surface free energy and the related Casimir force acting between the slit boundaries. Above the bulk condensation temperature (T>T_c) the Casimir force decays exponentially as a function of D with the bulk correlation length determining the relevant length scale. For T=T_c and for T4 and T\leq T_c., Comment: 7 pages

We consider homogeneous Bose gas in a large cubic box with periodic boundary conditions, at zero temperature. We analyze its excitation spectrum in a certain kind of a mean field infinite volume limit. We prove that under appropriate conditions the excitation spectrum has the form predicted by the Bogoliubov approximation. Our result can be viewed as an extension of the result of R. Seiringer (arXiv:1008.5349 [math-ph]) to large volumes., Comment: Revised and extended version. 26 pages, 4 figures. To appear in Annales Henri Poincar\'e