Inhomogeneous Condensates Research Articles (Page 1)

Abstract We investigate the dynamics of quantum vortex dipoles in a strongly interacting, spin-imbalanced Fermi superfluid at zero temperature. Using fully microscopic time-dependent density functional theory, we demonstrate that the dipole trajectory is strongly influenced by the spatial distribution of spin polarization. The resulting forces on the vortices include both longitudinal (dissipative) and transverse components, leading to deflection and shrinking of the dipole during propagation. For moderate polarization, vortex dipoles are deflected and lose energy, while for larger imbalances, they are rapidly annihilated. Our findings provide compelling evidence that spin-imbalanced Fermi gases contain a spatially nonuniform normal component even at zero temperature. We show that vortex dipoles serve as sensitive probes of this component, offering a route to indirectly detect exotic superfluid phases such as the Fulde–Ferrell–Larkin–Ovchinnikov state and related inhomogeneous condensates.

The Nambu-Goldstone modes on the exotic chiral condensed phase with chiral and tensor-type quark-antiquark condensates are investigated by using the two-point vertex functions. It is shown that one of the Nambu-Goldstone modes appears as a result of meson mixing. As is well known, another method to find the Nambu-Goldstone modes is given by the use of the algebraic commutation relations between broken generators and massless modes obtained through the spontaneous symmetry breaking. This method is adopted to the cases of the chiral symmetry breakings due to the tensor-type condensate and the inhomogeneous chiral condensate. The result obtained by the use of the meson two-point vertex functions is obviously reproduced in the case of the tensor-type condensate. Furthermore, we investigate the general rules for determining the broken symmetries and the Nambu-Goldstone modes algebraically. As examples, the symmetry breaking pattern and the Nambu-Goldstone modes due to the tensor-type condensate or the inhomogeneous chiral condensate are shown by adopting the general rules developed in this paper in the algebraic method. Published by the American Physical Society 2025

Dense quantum chromodynamics (QCD) matter may exhibit crystalline phases. Their existence is reflected in a moat regime, where mesonic correlations feature spatial modulations. We study the real-time properties of pions at finite temperature and density in QCD in order to elucidate the nature of this regime. We show that the moat regime arises from particle-hole-like fluctuations near the Fermi surface. This gives rise to a characteristic peak in the spectral function of the pion at nonzero spacelike momentum. This peak can be interpreted as a new quasi particle, the moaton. In addition, our framework also allows us to directly test the stability of the homogeneous chiral phase against the formation of an inhomogeneous condensate in QCD. We find that an inhomogeneous instability is highly unlikely for baryon chemical potentials μB≤630 MeV.

In the easy-plane phase, a ferromagnetic spin-1 Bose-Einstein condensate is magnetized in a plane transverse to the applied Zeeman field. This phase supports polar-core spin vortices (PCVs), which consist of phase windings of transverse magnetization. Here we show that spin-changing collisions cause a PCV to accelerate down density gradients in an inhomogeneous condensate. The dynamics is well-described by a simplified model adapted from scalar systems, which predicts the dependence of the dynamics on trap tightness and quadratic Zeeman energy. In a harmonic trap, a PCV accelerates radially to the condensate boundary, in stark contrast to the azimuthal motion of vortices in a scalar condensate. In a trap that has a local potential maximum at the centre, the PCV exhibits oscillations around the trap centre, which persist for a remarkably long time. The oscillations coincide with the emission and reabsorption of axial spin waves, which reflect off the condensate boundary.

We investigate the time evolution of the quark condensate toward a chiral symmetry broken phase in hot and dense quark matter using a field-theoretic quark model with nonlocal chiral-invariant four-fermion coupling. By purposely selecting a parameter set in which inhomogeneous phases are energetically disfavored, we nonetheless observe the emergence of metastable patterned configurations that appear to persist for remarkably long timescales. These findings suggest that even when not fully stable, inhomogeneous phases may play a significant role in the dynamics of chiral symmetry breaking and restoration. To gain deeper insight into these phenomena, we also analyze the impact of the dimensionality of coordinate space on both the formation and stability of inhomogeneous chiral condensates.

Abstract The tricritical behavior in a class of one-dimensional (1D) field theories that exhibit spontaneous symmetry breaking at zero temperature and chemical potential is analyzed. In the Gross–Neveu-type models of massless fermions the discrete chiral symmetry is spontaneously broken. After doping, the symmetry is restored at a critical chemical potential. We investigate the temperature effects on this doped 1D system under an externally constant Zeeman magnetic field B 0. We find that B 0 suppresses the gapless behavior present for certain values of chemical potential and is able to induce a gapless-gapped phase transition at a critical field strength. We also discuss the consequences of the consideration of inhomogeneous condensates at the tricritical point, within the Ginzburg–Landau expansion.

We investigate the dilepton production rates from annihilation processes of charged pion pairs with modified pion dispersion relations in the inhomogeneous chiral condensed phase. We assume a dual chiral density wave as an inhomogeneous chiral condensate, and obtain the dispersion relations of the Nambu-Goldstone modes in the inhomogeneous chiral condensed phase. We use a low energy effective Lagrangian based on the O(4) symmetry which is expanded by the order parameter up to the sixth order. The obtained dispersion relations are anisotropic and quadratic for the momentum. We evaluate the electron-positron production rates by charged pion-pair annihilations as functions of an invariant mass using the obtained dispersion relations. Basically, the production rate in the inhomogeneous chiral condensed phase has a steeper overall slope with respect to an invariant mass than that in the homogeneous chiral condensed phase. Therefore, the production rate may be enhanced when the invariant mass is around twice the pion mass. Published by the American Physical Society 2024

In this work we continue our efforts to study the existence of a phase with an inhomogeneous, i.e., spatially varying, chiral condensate in QCD. To this end we employ a previously established method of stability analysis of the two-particle irreducible effective action in a truncation that corresponds to a rainbow-ladder approximation of the quark-gluon interaction of QCD. If the analysis is restricted to homogeneous phases, the phase diagram features a first-order chiral transition in the lower-temperature regime. Performing the stability analysis along the lower-chemical-potential border of the corresponding spinodal region, we find that below a certain temperature the homogeneous chirally symmetric solution is unstable against inhomogeneous condensation. We argue that this instability may persist to chemical potentials above the homogeneous first-order phase boundary, in which case it signals the existence of an inhomogeneous ground state. Our methodology is also applicable for more sophisticated truncations of the QCD effective action. Published by the American Physical Society 2024

In this work, we demonstrate that the mixing of scalar and vector condensates produces spatially oscillating, but exponentially damped correlation functions in fermionic theories at finite density and temperature. We find a regime exhibiting this oscillatory behavior in a Gross-Neveu-type model that also features vector interactions within the mean-field approximation. The existence of this regime aligns with expectations based on symmetry arguments that are also applicable to QCD at finite baryon density. We compute the phase diagram including both homogeneous phases and regions with spatially oscillating, exponentially damped correlation functions at finite temperature and chemical potential for different strengths of the vector coupling. Furthermore, we find that inhomogeneous condensates are disfavored compared to homogeneous ones akin to previous findings without vector interactions. We show that our results are valid for a broad class of (2+1)-dimensional models with local four-fermion interactions. Published by the American Physical Society 2024

This work shows that the known phase boundary between the phase with chiral symmetry and the phase of spatially inhomogeneous chiral symmetry breaking in the phase diagram of the (1+1) -dimensional chiral Gross–Neveu (GN) model can be detected from the bosonic two-point function alone and thereby confirms and extends previous results (Schön and Thies 2000 At The Frontier of Particle Physics: Handbook of QCD, Boris Ioffe Festschrift vol 3 (World Scentific) ch 33, pp 1945–2032; Boehmer et al 2008 Phys. Rev. D 78 065043; Boehmer and Thies 2009 Phys. Rev. D 80 125038; Thies 2018 Phys. Rev. D 98 096019; Thies 2022 Phys. Rev. D 105 116003). The analysis is referred to as the stability analysis of the symmetric phase and does not require knowledge about spatial modulations of condensates. We perform this analysis in the infinite-N limit at nonzero temperature and nonzero quark and chiral chemical potentials also inside the inhomogeneous phase. Thereby we observe an interesting relation between the bosonic 1-particle irreducible two-point vertex function of the chiral GN model and the spinodal line of the GN model.

In this paper, we will review two analytical approaches to the construction of non-homogeneous Baryonic condensates in the low-energy limit of QCD in (3+1) dimensions. In both cases, the minimal coupling with the Maxwell U(1) gauge field can be taken explicitly into account. The first approach (which is related to the generalization of the usual spherical hedgehog ansatz to situations without spherical symmetry at a finite Baryon density) allows for the construction of ordered arrays of Baryonic tubes and layers. When the minimal coupling of the Pions to the U(1) Maxwell gauge field is taken into account, one can show that the electromagnetic field generated by these inhomogeneous Baryonic condensates is of a force-free type (in which the electric and magnetic components have the same size). Thus, it is natural to wonder whether it is also possible to analytically describe magnetized hadronic condensates (namely, Hadronic distributions generating only a magnetic field). The idea of the second approach is to construct a novel BPS bound in the low-energy limit of QCD using the theory of the Hamilton–Jacobi equation. Such an approach allows us to derive a new topological bound which (unlike the usual one in the Skyrme model in terms of the Baryonic charge) can actually be saturated. The nicest example of this phenomenon is a BPS magnetized Baryonic layer. However, the topological charge appearing naturally in the BPS bound is a non-linear function of the Baryonic charge. Such an approach allows us to derive important physical quantities (which would be very difficult to compute with other methods), such as how much one should increase the magnetic flux in order to increase the Baryonic charge by one unit. The novel results of this work include an analysis of the extension of the Hamilton–Jacobi approach to the case in which Skyrme coupling is not negligible. We also discuss some relevant properties of the Dirac operator for quarks coupled to magnetized BPS layers.

We continue previous investigations of the (inhomogeneous) phase structure of the Gross-Neveu model in a noninteger number of spatial dimensions (1≤d<3) in the limit of an infinite number of fermion species (N→∞) at (non)zero chemical potential μ [L. Pannullo, Inhomogeneous condensation in the Gross-Neveu model in noninteger spatial dimensions 1≤d<3, ]. In this work, we extend the analysis from zero to nonzero temperature T. The phase diagram of the Gross-Neveu model in 1≤d<3 spatial dimensions is well-known under the assumption of spatially homogeneous condensation with both a symmetry broken and a symmetric phase present for all spatial dimensions. In d=1 one additionally finds an inhomogeneous phase, where the order parameter, the condensate, is varying in space. Similarly, phases of spatially varying condensates are also found in the Gross-Neveu model in d=2 and d=3, as long as the theory is not fully renormalized, i.e., in the presence of a regulator. For d=2, one observes that the inhomogeneous phase vanishes, when the regulator is properly removed (which is not possible for d=3 without introducing additional parameters). In the present work, we use the stability analysis of the symmetric phase to study the presence (for 1≤d<2) and absence (for 2≤d<3) of these inhomogeneous phases and the related moat regimes in the fully renormalized Gross-Neveu model in the μ, T-plane. We also discuss the relation between “the number of spatial dimensions” and “studying the model with a finite regulator” as well as the possible consequences for the limit d→3. Published by the American Physical Society 2024

The first analytic solutions representing baryonic layers living at finite baryon density within a constant magnetic field in the gauged Skyrme model are constructed. A remarkable feature of these configurations is that, if the Skyrme term is neglected, then these baryonic layers in the constant magnetic background cannot be found analytically and their energies grow very fast with the magnetic field. On the other hand, if the Skyrme term is taken into account, the field equations can be solved analytically and the corresponding solutions have a smooth limit for large magnetic fields. Thus, the Skyrme term discloses the universal character of these configurations living at finite Baryon density in a constant magnetic field. The classical gran-canonical partition function of these configurations can be expressed explicitly in terms of the Pearcey integral. This fact allows us to determine analytically the Stokes lines of the partition function and the corresponding dependence on the baryonic chemical potential as well as on the external magnetic field. In this way, we can determine various critical curves in the (μB−Bext) plane which separates different physical behaviors. These families of inhomogeneous baryonic condensates can be also dressed with chiral conformal excitations of the solutions representing modulations of the layers themselves. Some physical consequences are analyzed.

Lattice Study of Disordering of Inhomogeneous Condensates and the Quantum Pion Liquid in Effective \(O(N)\) Model

Different classes of low-dimensional superconducting systems exhibit an inhomogeneous filamentary superconducting condensate whose macroscopic coherence still needs to be fully investigated and understood. Here, we present a thorough analysis of the superfluid response of a prototypical filamentary superconductor embedded in a two-dimensional metallic matrix. By mapping the system into an exactly solvable random impedance network, we show how the dissipative (reactive) response of the system non-trivially depends on both the macroscopic and microscopic characteristics of the metallic (superconducting) fraction. We compare our calculations with resonant microwave transport measurements performed on LaAlO_33/SrTiO_33 heterostructures over an extended range of temperatures and carrier densities finding that the filamentary character of superconductivity accounts for unusual peculiar features of the experimental data.

We investigate the propagation of electromagnetic radiation in the magnetic dual chiral density wave (MDCDW) phase of dense quark matter. Considering the theory of low-energy fluctuations in this phase, we show how linearly polarized photons reaching the MDCDW medium couple to the fluctuation field to produce two hybridized modes of propagation that we call in analogy with similar phenomenon in condensed matter physics axion polaritons, one of them being gapless and the other gapped. The gapped mode's gap is proportional to the background magnetic field and inversely proportional to the amplitude of the inhomogeneous condensate. The generation of axion polaritons can be traced back to the presence of the chiral anomaly in the low-energy theory of the fluctuations. Considering the Primakoff effect in the MDCDW medium, we argued that axion polaritons can be generated inside quark stars bombarded by energetic photons coming from gamma-ray bursts and point out that this mechanism could serve to explain the missing pulsar paradox in the galaxy center.

An in-depth understanding of liquid–liquid phase transition (LLPT) in condensed water will gain insight into anomalous behaviors of dual-amorphous condensed water. Despite numerous experimental, molecular simulation, and theoretical studies, it is yet to achieve a widely accepted consensus with convinced evidence in the condensed matter physics for two-state liquid–liquid transition of water. In this work, a theoretical model is proposed based on the Avrami equation, commonly used to describe first-order phase transitions, to elucidate complex homogeneous and inhomogeneous condensation from high-density liquid (HDL) water to low-density liquid (LDL) water for both pure and ionic dual-amorphous condensed water. This model unifies the coupling effects of temperature and electrolyte concentration based on the new theoretical framework. The Adam–Gibbs theory is then introduced to characterize the synergistic motion and relaxation behavior of condensed water. Variations in the configurational entropy under electrostatic forces are further explored, and an analytical 2D cloud chart is developed to visualize the synergistic effect of temperature and electrolyte concentration on the configurational entropy of ionic water. The constitutive relationships among viscosity, temperature, and electrolyte concentration are derived to analyze their synergistic effects under different condensation fractions of LDL and HDL. The Stokes–Einstein relation and free volume theory are further used to analyze diffusion coefficients and densities (or apparent density) during both pure and ionic LLPT. Finally, theoretical results obtained from these models are compared with experimental results reported in literature to validate the accuracy and applicability of the proposed models, which offer significant benefits and advancements in effectively predicting physical property changes of dual-amorphous condensed water.

In this paper, we will describe recent advances in analytical methods to construct exact solutions of the Skyrme model (and its generalizations) representing inhomogeneous Hadronic condensates living at finite Baryon density. Such novel analytical tools are based on the idea to generalize the well-known spherical hedgehog ansatz to situations (relevant for the analysis of finite density effects) in which there is no spherical symmetry anymore. Besides the intrinsic mathematical interest to find exact solutions with nonvanishing Baryonic charge confined to a finite volume, this framework opens the possibility to compute important physical quantities which would be difficult to compute otherwise.

We investigate inhomogeneous chiral condensation under rotation considering finite size effects and boundary conditions in the holographic QCD model. The rotational suppression effect determined by $\Omega r$ is confirmed in the holographic model which is not influenced by the boundary conditions. For chiral condensation at the center, it is found that under Neumann boundary condition the finite size exhibits two opposite effects, i.e., catalysis at high temperatures and inverse catalysis at low temperatures. In contrast, under Dirichlet boundary condition, the effect of finite size on condensation is inverse catalysis, and small size induces a phase transition from inhomogeneous to homogeneous phase. The temperature-angular velocity phase diagrams of QCD are obtained for different boundary conditions and sizes, and it is found that the critical temperature decreases with angular velocity.

The phase diagram of the (1 + 1)-dimensional Gross–Neveu model is reanalyzed for (non-)zero chemical potential and (non-)zero temperature within the mean-field approximation. By investigating the momentum dependence of the bosonic two-point function, the well-known second-order phase transition from the symmetric phase to the so-called inhomogeneous phase is detected. In the latter phase the chiral condensate is periodically varying in space and translational invariance is broken. This work is a proof of concept study that confirms that it is possible to correctly localize second-order phase transition lines between phases without condensation and phases of spatially inhomogeneous condensation via a stability analysis of the homogeneous phase. To complement other works relying on this technique, the stability analysis is explained in detail and its limitations and successes are discussed in context of the Gross–Neveu model. Additionally, we present explicit results for the bosonic wave-function renormalization in the mean-field approximation, which is extracted analytically from the bosonic two-point function. We find regions—a so-called moat regime—where the wave function renormalization is negative accompanying the inhomogeneous phase as expected.